LINEAR 1. Kendal bought x boxes of cookies to bring to a party. Each box contains 12 cookies. She decides to keep two boxes for herself. She brings 60 cookies to the party. Which equation can be used to find the number of boxes, x, Kendal bought? 2 A parking garage charges a base rate of $3.50 for up to 2 hours, and an hourly rate for each additional hour. The sign below gives the prices for up to 5 hours of parking. Which linear equation can be used to find x, the additional hourly parking rate? 3 John has four more nickels than dimes in his pocket, for a total of $1.25. Which equation could be used to determine the number of dimes, x, in his pocket? 4 A gardener is planting two types of trees: Type A is three feet tall and grows at a rate of 15 inches per year. Type B is four feet tall and grows at a rate of 10 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.
5 Donna wants to make trail mix made up of almonds, walnuts and raisins. She wants to mix one part almonds, two parts walnuts, and three parts raisins. Almonds cost $12 per pound, walnuts cost $9 per pound, and raisins cost $5 per pound. Donna has $15 to spend on the trail mix. Determine how many pounds of trail mix she can make. [Only an algebraic solution can receive full credit.] 6 Ian is borrowing $1000 from his parents to buy a notebook computer. He plans to pay them back at the rate of $60 per month. Ken is borrowing $600 from his parents to purchase a snowboard. He plans to pay his parents back at the rate of $20 per month. Write an equation that can be used to determine after how many months the boys will owe the same amount. Determine algebraically and state in how many months the two boys will owe the same amount. State the amount they will owe at this time. Ian claims that he will have his loan paid off 6 months after he and Ken owe the same amount. Determine and state if Ian is correct. Explain your reasoning. 7. If h represents a number, which equation is a correct translation of "Sixty more than 9 times a number is 375"? 8 Three times the sum of a number and four is equal to five times the number, decreased by two. If x represents the number, which equation is a correct translation of the statement? 9 The product of a number and 3, increased by 5, is 7 less than twice the number. Which equation can be used to find this number, n? 10 Rhonda has $1.35 in nickels and dimes in her pocket. If she has six more dimes than nickels, which equation can be used to determine x, the number of nickels she has?
11 Byron has 72 coins in his piggy bank. The piggy bank contains only dimes and quarters. If he has $14.70 in his piggy bank, which equation can be used to determine q, the number of quarters he has? 12 The width of a rectangle is 3 less than twice the length, x. If the area of the rectangle is 43 square feet, which equation can be used to find the length, in feet? 13 The length of a rectangular window is 5 feet more than its width, w. The area of the window is 36 square feet. Which equation could be used to find the dimensions of the window? 14 If n is an odd integer, which equation can be used to find three consecutive odd integers whose sum is? 15 The ages of three brothers are consecutive even integers. Three times the age of the youngest brother exceeds the oldest brother's age by 48 years. What is the age of the youngest brother? 14 18 22 26 16 The sum of three consecutive odd integers is 18 less than five times the middle number. Find the three integers. [Only an algebraic solution can receive full credit.
17. At the beginning of her mathematics class, Mrs. Reno gives a warm-up problem. She says, I am thinking of a number such that 6 less than the product of 7 and this number is 85. Which number is she thinking of? 11 13 84 637 18 If five times the measure of an angle is decreased by 30, the result is the same as when two times the measure of the angle is increased by 18. What is the measure of the angle? 16 4 19 Robin spent $17 at an amusement park for admission and rides. If she paid $5 for admission, and rides cost $3 each, what is the total number of rides that she went on? 12 2 9 4 20 Mario paid $44.25 in taxi fare from the hotel to the airport. The cab charged $2.25 for the first mile plus $3.50 for each additional mile. How many miles was it from the hotel to the airport? 10 11 12 13 21 If one-half of a number is 8 less than two-thirds of the number, what is the number? 24 32 48 54 22 A boy got 50% of the questions on a test correct. If he had 10 questions correct out of the first 12, and 16 24 26 28 of the remaining questions correct, how many questions were on the test?
23 Laura goes shopping. She spends one-fourth of her money on a pair of shorts, and onethird of her remaining money on a belt. If Laura has $42 left after these two purchases, how much money did she have when she started shopping? $84 $126 $144 $504 24 A total of $450 is divided into equal shares. If Kate receives four shares, Kevin receives three shares, and Anna receives the remaining two shares, how much money did Kevin receive? $100 $150 $200 $250 25 In his will, a man leaves one-half of his money to his wife, one-half of what is then left to his older child, and one-half of what is then left to his younger child. His two cousins divide the remainder equally, each receiving $2,000. What was the total amount of money in the man s will? $40,000 $32,000 $24,000 $16,000 26 During a recent winter, the ratio of deer to foxes was 7 to 3 in one county of New York State. If there were 210 foxes in the county, what was the number of deer in the county? 90 147 280 490 27 Sterling silver is made of an alloy of silver and copper in the ratio of. If the mass of a sterling silver ingot is 600 grams, how much silver does it contain? 48.65 g 200 g 450 g 555 g 28 There are 357 seniors in Harris High School. The ratio of boys to girls is. How many boys are in the senior class? 210 147 117 107
29 Every month, Omar buys pizzas to serve at a party for his friends. In May, he bought three more than twice the number of pizzas he bought in April. If Omar bought 15 pizzas in May, how many pizzas did he buy in April? 30 The sum of the ages of the three Romano brothers is 63. If their ages can be represented as consecutive integers, what is the age of the middle brother? 31 Sara s telephone service costs $21 per month plus $0.25 for each local call, and longdistance calls are extra. Last month, Sara s bill was $36.64, and it included $6.14 in longdistance charges. How many local calls did she make? 32 In a town election, candidates A and B were running for mayor. There were 30,500 people eligible to vote, and of them actually voted. Candidate B received of the votes cast. How many people voted for candidate B? What percent of the votes cast, to the nearest tenth of a percent, did candidate A receive? 33 There are 28 students in a mathematics class. If of the students are called to the guidance office, of the remaining students are called to the nurse, and, finally, of those left go to the library, how many students remain in the classroom? 34 After an ice storm, the following headlines were reported in the Glacier County Times: Monday: Ice Storm Devastates County 8 out of every 10 homes lose electrical power Tuesday: Restoration Begins Power restored to of affected homes Wednesday: More Freezing Rain Power lost by 20% of homes that had power on Tuesday Based on these headlines, what fractional portion of homes in Glacier County had electrical power on Wednesday? 35 The profits in a business are to be shared by the three partners in the ratio of 3 to 2 to 5. The profit for the year was $176,500. Determine the number of dollars each partner is to receive. 36 At the Phoenix Surfboard Company, $306,000 in profits was made last year. This profit was shared by the four partners in the ratio. How much more money did the partner with the largest share make than one of the partners with the smallest share?
37. Find three consecutive numbers whose sum is 9 greater than twice the largest number. 38. What number is that which being multiplied by 7 gives a product as much greater as the number itself is less than 20? 39. What number is that, the treble of which, increased by 12, shall as much exceed 54 as that treble is less than 144? 40. Find the number such that if 16 be subtracted from it, of the remainder will be equal to of the number. 41 A person expends $240 in the purchase of wheat. If he had paid 20 cents a bushel less he could have obtained 100 bushels more for the same money. How many bushels did he buy?