Open-Ended Application Problems Chapter Questions. 3. What is the formula for perimeter, area of a rectangle, area of a triangle?

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1 Open-Ended Application Problems Chapter Questions 1. List one strategy for solving a problem. 2. How would you define a consecutive integer? 3. What is the formula for perimeter, area of a rectangle, area of a triangle? 4. What relationship will help when solving percent problems? 5. List an example of a mixture type of problem. 6. What must be true of an object in uniform motion? 7. What is work rate? 8. What type of angles measure up to 90 degrees?

2 Open-Ended Application Problem Chapter Problems Number Problems Classwork 1) List three consecutive integers. 2) List four consecutive odd integers. 3) One number is 5 greater than another. If the lesser number is added to two times the greater number, the sum is 40. Find the numbers. 4) One number is 7 less than another. If the greater number is subtracted from three times the lesser number, the difference is 163. Find the greater number. 5) Find the largest of three consecutive even integers whose sum is 24. 6) Find two consecutive integers whose sum is 61. 7) The lengths of the sides of a triangle are consecutive integers. The perimeter is 36 meters. Find the length of the largest side. 8) The lengths of the sides of a triangle are consecutive odd integers. The perimeter is 81 meters. Find the length of all the sides. 9) Johnny has 7 less than three times as many pizza deliveries as when he started his route. If he currently has 56 stops, how many did he start with? 10) There are 68 marbles in a jar that contains only blue and red marbles. The number of blue marbles is 4 less than 5 times the number of red marbles. How many red marbles are in the jar? Homework 11) List five consecutive integers. 12) List four consecutive even integers. 13) One number is 35 less than another number. If the greater number is added to four times the lesser number, the sum is 100. Find the numbers. 14) One number is 8 more than another. If the greater number is added to five times the lesser number, their sum is 44. Find the greater number. 15) Find the smallest of three consecutive even integers whose sum is 99.

3 16) Find two consecutive even integers whose sum is ) The lengths of the sides of a triangle are consecutive integers. The perimeter is 15 meters. Find the length of the largest side. 18) The lengths of the sides of a triangle are consecutive even integers. The perimeter is 42 meters. Find the length of all the sides. 19) Mary has 3 more than three times as many shopping bags as when she started shopping at the mall hours ago. If she currently has 21 bags, how many did she start with? 20) There are 300 marbles in a jar that contains only blue and red marbles. The number of blue marbles is 20 less than 4 times the number of red marbles. How many red marbles are in the jar? Age Problems Classwork Complete the table for each: 21) Joanna is 5 years older than her cat. Next year she will be three times as old as her cat will be. How old is her cat? 22) Eric is now ten years older than his niece Michelle. In five years, Eric will be four times Michelle s present age. Find the age that Eric will be in five years.

4 23) In four years, Billy will be twice the age of Diana. If he is now seven years older than her, what is the age of each person now? Write an Open Sentence for the following: 24) Tina is twice as old as Shelly. The sum of their ages is 65. How old is Tina? 25) Shelly is four times as young as Martha. The sum of their ages is 99. How old is Martha? 26) The daughter is 30 years younger than her mother. The sum of their ages is 72. How old is mom? Solve: 27) Ricky s age is nine years greater than twice Bobby s age. If the sum of their ages is 21, how old are the boys? 28) Julie s age is 15 years less than three times Frank s age. If the sum of their ages is 5, how old is Frank? 29) There are three brothers in a store. Each brother is two years older than the next. The oldest brother is twice as old as the youngest brother. What is the age of the brothers? 30) There are five sisters at home. Each sister is three years older than the next. The oldest sister is four times the age of the youngest sister. What is the age of the oldest sister? Homework Complete the table for each: 31) Linda is 6 years older than her hamster. Next year she will be 4 times as old as the hamster. How old is Linda?

5 32) John is now twelve years older than his brother Timmy. In two years, John will be five times Timmy s age. Find the age Timmy will be in two years. 33) In three years, Jenna will be two times the age of Hannah. If Jenna is now seven years older than Hannah, how old will they both be? Write an Open Sentence for the following: 34) Bobby is three times as old as Kelly. The sum of their ages is 46. How old is Bobby? 35) Lisa is three times as young as Jackie. The sum of their ages is 110. How old is Jackie? 36) The son is three times younger than his father. The sum of their ages is 40. How old is the son? Solve: 37) Tammy s age is seven years greater than four times Jordan s age. If the sum of their ages is 57, how old are the girls? 38) Lauren s age is 11 years more than four times Robert s age. If the difference of the smaller age from the larger age is 26, how old is Lauren? 39) There are four brothers in a store. Each brother is two years older than the next. The youngest brother is three times as young as the oldest brother. What is the age of the brothers? 40) There are five sisters at home. Each sister is one year older than the next. The oldest sister is five times the age of the youngest sister. What is the age of the third youngest sister?

6 Geometry Problems Classwork 41) What is the perimeter of a square with one side length of 4? 42) What is the perimeter of a triangle with side lengths of 5,7, and 9? 43) What is the area of a rectangle with side lengths of 4 and 8? 44) What is the area of a triangle with a base of 4 and a height of 8? 45) A square has its side tripled in length. How much does the area of the square increase? 46) The length of a pool is two more feet than twice the width. The area of the pool is 36 feet. What is the length of the garden in terms of width? 47) A kitchen floor s length is 4 feet less than five times its width. The area of the kitchen is 100 feet. What is the length of the kitchen in terms of the width? 48) The measure of the perimeter of a square is 16a + 40b. What is the measure of the area of the square? Find the area of the white region below (not green): 49) x + 8 6x x + 2 3x 50) 13x 2x

7 Homework 51) What is the perimeter of a square with one side length of 7? 52) What is the perimeter of a triangle with side lengths of 8, 9 and 10? 53) What is the area of a rectangle with side lengths of 10 and 12? 54) What is the area of a triangle with a base of 10 and a height of 12? 55) A square has its side quadrupled in length. How much does the area of the square increase? 56) The length of a pool is four more feet than three times the width. The area of the pool is 56 feet. What is the length of the garden in terms of width? 57) A kitchen floor s length is 8 feet less than five times its width. The area of the kitchen is 69 feet. What is the length of the kitchen in terms of width? 58) The measure of the perimeter of a square is 4a + 28b. What is the measure of the area of the square? Find the area of the white region below (not green): 59) x x 8x x ) x + 9 3x 2 x 4x

8 Percent Problems Classwork 61) A shirt is on the rack for $ There is a 15% discount that day in the store. What amount of money will come off of the original price? 62) A dress is on sale for $60.00 after a 50% discount is taken off. What is the regular price of the dress? 63) A new bike is $ in the store. There is a 7% tax in the store. How much will you pay for the bike? 64) The bill at the restaurant is $46. You want to leave a 30% tip. How much will you leave for the tip? 65) The first store has a TV for $1100 on sale 30% off. A second store has the same TV for $1100 on sale for 10% with an additional 20% with your coupon you have. Which store has the better deal? 66) A DVD movie price increases from $15.00 to $ What is the percent of increase? 67) How much is the percent of change when the original price of a bathing suit is $300 and the new price is $50? 68) How much will simple interest be if the Johnson s invest $30,000 at 5% interest rate for 6 years? 69) The Smiths paid $15,000 in closing costs when buying their first new home. If this amount represents 7% of the purchase price, how much did they pay for their home? 70) Karin invested part of $9,000 in one bank account that pays 5% simple annual interest and the rest in an account that pays 9% simple annual interest. How much money is invested in each account if the total annual income is $600? Homework 71) A skirt is on the rack for $ There is a 43% discount that day in the store. What amount of money will come off of the original price? 72) A suit is on sale for $67.72 after a 50% discount is taken off. What is the regular price of the suit? 73) A new grill is $ in the store. There is a 7.75% tax in the store. How much will you pay for the grill? 74) The bill at the restaurant is $ You want to leave a 15% tip. How much will you leave for the tip? 75) The first store has a computer for $2100 on sale 30% off. A second store has the same computer for $2100 on sale for 10% with an additional 40% with your coupon you have. Which store has the better deal?

9 76) An itunes movie price increases from $10.00 to $ What is the percent of increase? 77) How much is the percent of change when the original price of a dress is $200 and the new price is $50? 78) How much will simple interest be if the Linders invest $30,000 at 9% interest rate for 4 years? 79) The Farleys paid $10,000 in closing costs when buying their first new home. If this amount represents 5% of the purchase price, how much did they pay for their home? 80) Thomas invested part of $10,000 in one bank account that pays 5% simple annual interest and part in an account that pays 9% simple annual interest. How much money is invested in each account if the total annual income is $625? Mixture Problems Classwork Set Up the following problems in the table: 81) Andrew bought some apples worth $0.98 and some bananas worth $0.57. He bought 24 fruit items in total and paid $15.00 for them. How many apples and bananas did he buy? 82) Phil was conducting an experiment with a 30L solution that was 12% salt. How much water must be added to make it a 5% salt solution? Solve: 83) Alexis was conducting an experiment with a 24L solution that was 15% salt. How much water must be added to make it a 7% salt solution?

10 84) A ticket booth sold 226 tickets and collected $843 in ticket sales. Adult tickets are $5.50 and child tickets are $1.50. How many tickets for adults were sold? 85) A 12L solution is 50% oil. How much water must be added to produce a solution that is 45% oil? 86) Madison has three times as many dimes as pennies in her piggy bank. If the dimes and pennies total $8.37, how many pennies does she have? 87) The register at the grocery store has 15 bills in $5 and $10 denominations. The value of the money in the register is $100. How many $10 bills are in the register? 88) How many gallons of a 3% salt solution must be mixed with 50 gallons of a 7% solution to obtain a 5% solution? 89) A 50 ml after-shave lotion at 30% alcohol is mixed with 30 ml of pure water. What is the percentage of alcohol in the new solution? 90) How many pounds of chocolate worth $1.20 a pound must be mixed with 10 pounds of chocolate worth 90 cents a pound to produce a mixture worth $1.00 a pound? Homework Set Up the following problems in the table: 91) Susan bought some peanuts worth $0.64 and some cashews worth $0.32. He bought 26 nuts in total and paid $14.40 for them. How many peanuts did he buy? 92) Tiffany was conducting an experiment with a 44L solution that was 13% salt. How much water must be added to make it a 2% salt solution?

11 Solve: 93) Alexa was conducting an experiment with a 48L solution that was 22% salt. How much water must be added to make it a 15% salt solution? 94) How many pounds of chocolate worth $4.50 a pound must be mixed with 10 pounds of chocolate worth $3.90 a pound to produce a mixture worth $4.00 a pound? 95) How many gallons of a 4% salt solution must be mixed with 20 gallons of a 10% solution to obtain a 7% solution? 96) Margaret has 3 more than 2 times as many dimes as pennies in her piggy bank. If the dimes and pennies total $0.75, how many pennies does she have? 97) Five hundred tickets were sold for a certain music concert. The tickets for the adults and children sold for $7.50 and $4.00, respectively, and the total receipts for the performance were $3, How many child tickets were sold? 98) How many liters of 20% alcohol solution should be added to 40 liters of a 50% alcohol solution to make a 30% solution? 99) Sterling Silver is 92.5% pure silver. How many grams of Sterling Silver must be mixed to a 90% Silver alloy to obtain a 500g of a 91% Silver alloy? 100) How many Kilograms of Pure water is to be added to 100 Kilograms of a 30% saline solution to make it a 10% saline solution. Uniform Motion Problems Classwork 101) Two airplanes leave from the same airport at the same time traveling to Hawaii. The faster plane arrives in 5 hours. The slower plane arrives in 15 hours. The slower plane travels at an average speed that is 25km/h slower than the faster plane. What is the average speed of the faster plane? 102) Ariel and Sam are 545 meters apart. Ariel walks towards Sam at a rate of 1.7 m/s and Sam starts running towards Ariel. What is Sam s rate of travel is she reaches Ariel in 2 minutes? 103) Fred is a member of the swim team at school. On Tuesday he swam towards the far side of the pool at a rate of 4.6 m/min and on the return back he swam at a rate of 3.4 m/min. If he took 7 minutes to swim the entire distance, how long is the pool? 104) Sarah made the trip in 10 hours, but it only took Alice 8 hours to make the same trip. Find Sarah s rate of speed if Alice's rate was 3 mph more than Sarah's rate.

12 105) The bus made the trip in 6 hours, but the train took only 4 hours for the same trip. Find the rate of the bus if the train's rate of speed is 25 mph more than the bus' rate. 106) A car and a bus set out at 2 p.m. from the same point, headed in the same direction. The average speed of the car is 30 mph slower than twice the speed of the bus. In two hours, the car is 20 miles ahead of the bus. Find the rate of the car. 107) Two trains start from the same station and run in opposite directions. One runs at an average rate of 40 miles per hour, and the other at 65 miles per hour. In how many hours will they be 315 miles apart? 108) Mr. Williams starts out in his auto traveling 30 miles per hour. Four hours later Mr. Speedster starts out from the same point at 60 miles per hour to overtake Mr. Williams. In how many hours will he be overtaken? 109) A pilot flew to Newark and back. The average speed going was 320 mph. The average speed returning was 480 mph. Find the distance to Newark if the total flying time was 5h. 110) A car and a bus set out at 3 p.m. from the same point headed in the same direction. The average speed of the car is twice the average speed of the bus. In 2 h, the car is 68 mi ahead of the bus. Find the rate of the car. Homework 111) Two sail boats leave from the same port at the same time traveling to Jamaica. The faster boat arrives in 4 hours. The slower boat arrives in 6 hours. The slower boat travels at an average speed that is 2km/h slower than the faster boat. What is the average speed of the faster boat? 112) Miriam and Doug are 700 meters apart. Doug walks towards Miriam at a rate of 3.4 m/s and Miriam starts running towards Doug. What is Miriam's rate of travel if she reaches Doug in 1.4 minutes? 113) Francine is a member of the track team at school. On Thursday he ran towards the far side of the track at a rate of 3.5 m/hr and on the return back he ran at a rate of 5 m/hr. If he took 10 minutes to run the entire distance, how long is the track? 114) Shannon made the trip in 20 hours, but it only took Alicia 16 hours to make the same trip. Find Alicia s rate if her rate was 6 mph more than Shannon's rate. 115) The bus made the trip in 8 hours, but the train took only 3 hours for the same trip. Find the rate of the bus if the train's rate of speed is 35 mph more than the bus' rate. 116) A car and a bus set out at 5 p.m. from the same point, headed in the same direction. The average speed of the car is 40 mph slower than twice the speed of the bus. In three hours, the bus is 10 miles ahead of the car. Find the rate of the car.

13 117) Two trains start from the same station and run in opposite directions. One runs at an average rate of 50 miles per hour, and the other at 70 miles per hour. In how many hours will they be 200 miles apart? 118) Mr. Sanford starts out in his truck traveling 40 miles per hour. Three hours later Mr. Shocker starts out from the same point at 65 miles per hour to overtake Mr. Williams. In how many hours will he be overtaken? 119) A pilot flew to New York and back. The average speed going was 450 mph. The average speed returning was 380 mph. Find the distance to New York if the total flying time was 4h. 120) A van and a truck set out at 1 p.m. from the same point headed in the same direction. The average speed of the van is twice the average speed of the truck. In 3 hours, the van is 105 mi ahead of the truck. Find the rate of the truck. Work Problems Classwork 121) Max can paint a room in 3 hours. Matt can paint the same room in 2 hours. How long would it take them to paint the room if they worked together? 122) Julia can paint a room in 7 hours. Agatha can paint the same room in a different amount of time. If together they paint the room in 4 hours, how fast can Agatha paint a room? 123) Katie can make a cake in 2 hours. Amanda can make a cake in 4 hours. How long would it take to make a cake if both of the girls worked together? 124) Nicole can wash her car in 20 minutes. Anna can wash her car in 1 hour. If they worked together to wash the same car, how long would it take them to wash it? 125) Meghan can clean her room in a certain amount of time. Molly can clean her room in 3 hours. If it takes Meghan and Molly 2 hours to clean their room, in how much time could it take Meghan to clean the room by herself? 126) Langston and Roger can write a song together in 4 hours. Alone, it takes Langston 6 hours to write one. How long does it take Roger to write a song by himself? 127) Mom can sew a button back on in 5 minutes. Aunt Miriam can sew a button on in 15 minutes. How long would it take mom and Aunt Miriam to sew on one button together? Is it faster than just mom sewing on the button? 128) It takes five hours for a hose to fill up a swimming pool. It takes 2 hours for a newer hose to fill up the same swimming pool. How long would it take to fill the pool if both hoses were being used?

14 129) Maid Maria can clean a hotel room in 30 minutes while maid Rachel can clean a hotel room in 50 minutes. If both maids are cleaning the same hotel room at the same time, how long would it take for the room to get clean? 130) Isabella takes 2 hours to pick apples. Ronnie takes 30 minutes to pick apples. How long would it take both of them to pick apples together? Homework 131) Minnie can paint a room in 4 hours. Mickey can paint the same room in 7 hours. How long would it take them to paint the room if they worked together? 132) Gianna can paint a room in 8 hours. Aretha can paint the same room in a different amount of time. If together they paint the room in 5 hours, how fast can Agatha paint a room? 133) My sister can make cookies in 3 hours. My brother can make them in 4 hours. How long would it take to make cookies if they both worked together? 134) Elvis can wash his car in a half an hour. Marilyn can wash her car in one and a half hours. If they worked together to wash the same car, how long would it take them to wash it? 135) Harry can clean his desk in a certain amount of time. Harmony can clean her desk in 30 minutes. If it take Harry and Harmony 10 minutes to clean their desks, in how much time could it take Meghan to clean the desk by herself? 136) Maureen and David can write a story together in 8 days. Alone, it takes Maureen 9 days to write one. How long does it take David to write a story by himself? 137) Sara can knit a scarf in 45 minutes. Katherine can knit a scarf in 1 hour. How long would it take Sara and Katherine to knit one scarf together. Is it faster than just Sara knitting one? 138) It takes six hours for a hose to fill up a swimming pool. It takes 3 hours for a newer hose to fill up the same swimming pool. How long would it take to fill the pool if both hoses were being used? 139) Maid Delia can clean a hotel in 30 hours while maid Lori can clean a hotel in 50 hours. If both maids are cleaning the same hotel at the same time, how long would it take for the whole hotel to get clean? 140) Isabella takes 2 hours to pick oranges. Ronnie takes 1.5 hours to pick oranges. How long would it take both of them to pick oranges together? Proportionality Problems Classwork 141) Mr. Thompson bought 15 pounds of cement to cover his walkway with an area of 100 square feet. At this rate, how much cement would he need to cover 1000 square feet?

15 142) The measure of two complimentary angles are in the ratio 4:5. Find the measure of each angle in degrees. 143) The measure of two supplementary angles are in the ratio 6:9. Find the measure of each angle in degrees. 144) A high school has 5000 students, where 5 out of 8 students said that they don t want recess. How many students do want recess. 145) A 5 pound cake recipe calls for 3 eggs. At this rate, how many eggs will be needed for a 10 pound cake? 146) The scale on a treasure map is 2 inches to 7 miles. If the road to the treasure is 6 inches on the map, how long is the road in real life? 147) The scale on a blueprint for a bathroom is 1 inch to 4 feet. If the bathroom on the blueprint is 4.5 inches by 3 inches, what is the area of the actual bathroom? 148) The measures of two adjacent angles are in the ratio of 3 to 5. If the sum of the angle measures is 88, what is the measure of the smaller angle? 149) The measure of two supplementary angles are in the ratio of 2:14. Find the measure of the larger angle. 150) The ratio of dogs to cats in the pet store is 8:3. If there are 55 pets in the store, how many dogs are there? Homework 151) Mr. Woods bought 2 pounds of concrete to cover his sidewalk with an area of 5 square feet. At this rate, how much concrete would he need to cover 10 square feet? 152) The measure of two complimentary angles are in the ratio 7:13. Find the measure of each angle in degrees. 153) The measure of two supplementary angles are in the ratio 4:12. find the measure of each angle in degrees. 154) A high school has 2000 students, where 5 out of 8 students said that they do want soda in the cafeteria. How many students do not want soda. 155) A 14 pound soup recipe calls for 4 eggs. At this rate, how many eggs will be needed for a 20 pound soup? 156) The scale on a hunting map is 3 inches to 7 miles. If the road to the bears is 6 inches on the map, how long is the road in real life?

16 157) The scale on a blueprint for a kitchen is 1 inch to 3.5 feet. If the bathroom on the blueprint is 6 inches by 9 inches, what is the area of the actual kitchen? 158) The measures of two adjacent angles are in the ratio of 5 to 11. If the sum of the angle measures is 100, what is the measure of the smaller angle? 159) The measure of two supplementary angles are in the ratio of 5:10. Find the measure of the larger angle? 160) The ratio of birds to fish in the pet store is 2:38. If there are 440 pets in the store, how many fish are there?

17 Answer Key 1. answers will vary 2. answers will vary and and meters 8. 25, 27 and 29 meters stops red marbles 21. Age Now Age Next Year 11. answers will vary 12. answers will vary and , , 14 and bags red marbles Cat X x + 1 Joanna x + 5 (x + 5) + 1 The cat is 1.5 year old. 22. Age Now Age in 5 years Eric x + 10 (x + 10) + 5 Michelle x x + 5 Eric will be 20 years old in 5 years. 23. Age Now Age in 4 years Billy x + 7 (x + 7) + 4 Diana X x + 4 Diana is 3 years old and Billy is 10 years old. 24. x + 2x = x + 4x = x - 30 = 72 (or) x + x - 30 = Bobby is 4 and Ricky is Frank is the brothers are 4, 6 and

18 31. Age Now Age Next Year Hamster x + 6 (x + 6) + 1 Linda x x + 1 Linda is 7 years old. 32. Age Now Age in 2 years John x + 12 (x + 12) + 2 Timmy X x + 2 Timmy will be Age Age in 3 years Jenna x + 7 (x+7) + 3 Hannah X x + 3 Jenna will be 14, Hannah will be x + 3x = 46 (or) 4x = x + 3x = 110 (or) 4x = x + 3x = 40 (or) 4x = Jordan is 10 and Tammy is Robert is 5 and Lauren is the brothers are 3, 5, 7, and years old units units units units times 46. l = 2w l = 5w (16a ab + 100b 2 ) units x x x units units units units times 56. l = 3w l = 5w (a ab + 49b 2 ) units x 2 +48x units x x 2 units $ $ $ $ The first store % increase % decrease 68. $ $214, $5250 at 5% and $3750 at 9% 71. $ $ $ $ the 2nd store % increase % decrease

19 78. $10, $200, $6,875 at 5% and $3,125 at 9% 81. Number of Fruit Price of Fruit Total Value Apples s $ s Bananas 24 - s $ (24 - s) Mixture 24 $ apples and 20.8 bananas 82. Volume of Solution % Salt Volume of Salt Original Solution 30 12%.12(30) Water Added s 0% 0(s) = 0 New Solution 30 + s 5% 0.05(30 + s) 42 L of water added L adult tickets L pennies 87. 5, $10 bills gallons % pounds peanuts 92. Number of Nut Price of Nut Total Value Peanuts s $ s Cashews 26 - s $ (26 - s) Mixture 26 $14.40 Volume of Solution % Salt Volume of Salt Original Solution 44 13% 0.13(44) Water Added s 0% 0(s) = 0 New Solution 44 + s 2% 0.02(44 + s) 242L water

20 L pounds of chocolate gallons pennies child tickets liters grams kilograms km/h m/s meters mph mph mph hours hours miles mph km/h m/s miles mph mph mph hours hours miles mph hours hours hours minutes hours hours minutes, yes hours minutes minutes hours hours hours minutes minutes days minutes, yes hours hours hour pounds degrees & 50 degrees degrees & 108 degrees students eggs miles feet degrees degrees dogs pounds degrees & 58.5 degrees degrees & 135 degrees students eggs miles feet degrees degrees fish