Lesson 4.3 Real-World Problems: Ratios Solve. Example The ratio of Harry s money to Lincoln s money is 6 : 5. a) If Harry and Lincoln have a total of $715, how much money does Harry have?? Harry Lincoln $715 Total amount of money 5 6 1 5 5 11 units 11 units $ 715 1 unit $ 715 4 11 5 $ 65 6 units 6 3 $ 65 5 $ 390 Harry has $ 390. b) If Lincoln has $575, how much money does Harry have?? Harry Lincoln $575 5 units $ 575 1 unit $ 575 4 5 5 $ 115 6 units 6 3 $ 115 5 $ 690 Harry has $ 690. Reteach Course 1A 105
1. A box contains red ink pens and blue ink pens. The ratio of the number of red ink pens to the number of blue ink pens is 6 : 1. a) If the total number of ink pens is 1,932, find the number of each type of ink pens. Red Blue 1,932 Total number of ink pens 5 1 5 units units unit 4 5 The box contains red ink pens and blue ink pens. b) If the number of red ink pens is 858, find the number of blue ink pens. 858 Red Blue? units unit 4 5 The box contains blue ink pens. 106 Chapter 4 Lesson 4.3
2. A wooden plank is cut into two pieces. The ratio of the length of the two pieces of wood is 7 : 10. a) If the length of the original wooden plank is 952 centimeters, what is the length of the shorter piece of wood? b) If the length of the shorter piece of wood is 168 centimeters, what is the length of the longer piece of wood? Reteach Course 1A 107
Solve. Example The ratio of the number of orange trees to the number of apple trees to the number of pear trees in an orchard is 5 : 6 : 4. a) If there are 1,275 trees in the orchard, how many of each type of fruit trees are there? Orange Apple 1,275 trees Pear Total number of units 5 5 1 6 1 4 5 15 15 units 1,275 1 unit 1,275 4 15 5 85 5 units 5 3 85 5 425 There are 425 orange trees. 6 units 6 3 85 5 510 There are 510 apple trees. 4 units 4 3 85 5 340 There are 340 pear trees. 108 Chapter 4 Lesson 4.3
b) If there are 720 pear trees, how many trees are there in all? Orange Apple? Pear 720 trees 4 units 720 1 unit 720 4 4 5 180 15 units 15 3 180 5 2,700 There are 2,700 trees in all. 3. Shelby, Brandon, and Ling shared the cost of lunch in the ratio 2 : 5 : 3. a) If lunch cost $250, how much did each person pay? Total number of units 5 1 1 5 units Shelby Brandon Ling $250 unit 4 5 Shelby paid. Brandon paid. Ling paid. Reteach Course 1A 109
b) If Ling paid $24, how much did the lunch cost? Shelby Brandon? Ling $24 units unit 4 5 The lunch cost. 4. The number of stickers collected by Maurice, Elle, and Justin is in the ratio 8 : 5 : 7. a) If Maurice collected 960 stickers, how many stickers did Elle and Justin each collect? b) If the three children have 1,500 stickers altogether, how many stickers did they each collect? 110 Chapter 4 Lesson 4.3
Solve. Example In a school, the ratio of the number of girls to the number of boys is 7 : 5. In the same school, the ratio of the number of boys to the number of teachers is 15 : 1. There are 210 girls in the school. How many boys and teachers are there? 210 Girls Girls Boys Boys Teachers Girls : Boys 5 7 : 5 3 3 3 3 Boys : Teachers 5 15 : 1 5 21 : 15 So, Girls : Boys : Teachers 5 21 : 15 : 1 21 units 210 1 unit 210 4 21 5 10 15 units 15 3 10 5 150 There are 150 boys and 10 teachers. Reteach Course 1A 111
5. The ratio of the number of hair clips to the number of ribbons is 5 : 2. The ratio of the number of ribbons to the number of headbands is 4 : 5. If there are 40 hair clips, how many ribbons and headbands are there? 40 Hair clips Hair Clips Ribbons Ribbons Headbands Hair clips : Ribbons 5 5 : 2 Ribbons : Headbands 5 : 3 3 5 : So, Hair clips : Ribbons : Headbands 5 : : units unit 4 5 There are ribbons and headbands. 112 Chapter 4 Lesson 4.3
6. The ratio of the number of red marbles to the number of green marbles in a bag is 2 : 3. The ratio of the number of green marbles to the number of blue marbles is 9 : 4. There are 76 marbles in the bag. a) Find the number of red marbles in the bag. b) Find the number of green marbles in the bag. c) Find the number of blue marbles in the bag. Reteach Course 1A 113
Solve. Example In the morning, the ratio of the number of seabirds to the number of sea turtles in a rescue center is 3 : 2. After 15 sea turtles are rescued in the afternoon, the ratio becomes 9 : 11. Before The ratio of the number of seabirds to the number Seabirds of sea turtles is 3 : 2. Sea turtles After The ratio of the number of seabirds to the number of sea turtles becomes 9 : 11. The number of seabirds does not change. So, the length of the model for seabirds does not change. The model for seabirds is divided into 9 units. The model for sea turtles is divided into units of the same size and additional units are added to make the total length 11 units. The additional units represent the 15 sea turtles rescued in the afternoon. Seabirds Sea turtles 15 a) How many seabirds are in the rescue center? 5 units 15 1 unit 15 4 5 5 3 9 units 9 3 3 5 27 There are 27 seabirds in the rescue center. 114 Chapter 4 Lesson 4.3
b) How many sea turtles are in the rescue center in the afternoon? 11 units 11 3 3 5 33 There are 33 sea turtles in the rescue center in the afternoon. 7. The ratio of the number of newspapers Joshua sold to the number of newspapers Ron sold was 5 : 3. After Ron sold 28 more newspapers in the evening, the ratio became 10 : 13. Before The ratio of the number of newspapers Joshua sold to the number of newspapers Ron sold was :. Joshua Ron After The ratio of the number of newspapers Joshua sold to the number of newspapers Ron sold became :. The length of the model for does not change. The model for is divided into units. The model for Ron is divided into units of the same size and additional units are added to make the total length units. The additional units represent the newspapers Ron sold in the evening. Joshua Ron 28 Reteach Course 1A 115
a) How many newspapers did Joshua sell? units unit 4 5 Joshua sold newspapers. b) How many newspapers did Ron sell in all? Ron sold newspapers in all. 8. The ratio of the number of boys to the number of girls in a dance club is 5 : 6. After 6 more boys join the club, the ratio became 13 : 12. a) How many members of the club are girls? b) How many boys are members of the club in the end? 116 Chapter 4 Lesson 4.3