1 Scale To Amount Set 1

Question 1

1. A model car is 1/24 the size of a real car. If the real car is 20 feet long, how long is the model car?

Answer 1

The model car is 10 inches long. Explanation: If the real car is 20 feet long and the model car is 1/24 the size, we can set up a proportion: 20 feet / 24 = x inches / 1. Simplifying the left side: 20 / 24 = 5 / 6. So, the equation becomes: 5/6 = x / 1. Multiplying both sides by 1, we get: x = 5/6 inches = 10 inches (since 1 foot = 12 inches).

Question 2

2. A map has a scale of 1 inch = 50 miles. If two cities are 4 inches apart on the map, how far apart are they in real life?

Answer 2

The two cities are 200 miles apart. Explanation: If 1 inch on the map represents 50 miles in real life, we can set up a proportion: 1 inch / 50 miles = 4 inches / x miles. Cross-multiplying, we get: 1 inch * x miles = 4 inches * 50 miles. Simplifying the right side: 4 inches * 50 miles = 200 miles. So, the equation becomes: 1 inch * x miles = 200 miles. Dividing both sides by 1 inch, we get: x = 200 miles.

Question 3

3. A recipe calls for 1 cup of sugar to make 12 cookies. How many cups of sugar are needed to make 48 cookies?

Answer 3

4 cups of sugar are needed. Explanation: If 1 cup of sugar is needed to make 12 cookies, we can set up a proportion: 1 cup / 12 cookies = x cups / 48 cookies. Cross-multiplying, we get: 1 cup * 48 cookies = 12 cookies * x cups. Simplifying the left side: 48 = 12 * 4. So, the equation becomes: 48 = 4 * x cups. Dividing both sides by 4, we get: x = 12 cups.

Question 4

4. A model airplane is 1/72 the size of a real airplane. If the real airplane has a wingspan of 100 feet, what is the wingspan of the model airplane?

Answer 4

The wingspan of the model airplane is approximately 16.7 inches. Explanation: If the real airplane has a wingspan of 100 feet and the model airplane is 1/72 the size, we can set up a proportion: 100 feet / 72 = x inches / 1. Simplifying the left side: 100/72 = 25/18. So, the equation becomes: 25/18 = x / 1. Multiplying both sides by 1, we get: x = 25/18 inches = 1.39 feet = approximately 16.7 inches.

Question 5

5. A map has a scale of 1 inch = 100 miles. If two cities are 5 inches apart on the map, how far apart are they in real life?

Answer 5

The two cities are 500 miles apart. Explanation: If 1 inch on the map represents 100 miles in real life, we can set up a proportion: 1 inch / 100 miles = 5 inches / x miles. Cross-multiplying, we get: 1 inch * x miles = 5 inches * 100 miles. Simplifying the right side: 5 inches * 100 miles = 500 miles. So, the equation becomes: 1 inch * x miles = 500 miles. Dividing both sides by 1 inch, we get: x = 500 miles.

Question 6

6. A recipe calls for 3 cups of flour to make 24 cookies. How many cups of flour are needed to make 36 cookies?

Answer 6

4.5 cups of flour are needed. Explanation: If 3 cups of flour are needed to make 24 cookies, we can set up a proportion: 3 cups / 24 cookies = x cups / 36 cookies. Cross-multiplying, we get: 3 cups * 36 cookies = 24 cookies * x cups. Simplifying the left side: 3 * 36 = 108. So, the equation becomes: 108 = 24 * x cups. Dividing both sides by 24, we get: x = 4.5 cups.

Question 7

7. A model train is 1/87 the size of a real train. If the real train is 200 feet long, how long is the model train?

Answer 7

The model train is approximately 27.59 inches long. Explanation: If the real train is 200 feet long and the model train is 1/87 the size, we can set up a proportion: 200 feet / 87 = x inches / 1. Simplifying the left side: 200/87 is approximately 2.30. So, the equation becomes: 2.30 = x / 1. Multiplying both sides by 1, we get: x = 2.30 inches = approximately 27.59 inches.

Question 8

8. A map has a scale of 1 inch = 500 miles. If two cities are 2 inches apart on the map, how far apart are they in real life?

Answer 8

The two cities are 1000 miles apart. Explanation: If 1 inch on the map represents 500 miles in real life, we can set up a proportion: 1 inch / 500 miles = 2 inches / x miles. Cross-multiplying, we get: 1 inch * x miles = 2 inches * 500 miles. Simplifying the right side: 2 inches * 500 miles = 1000 miles. So, the equation becomes: 1 inch * x miles = 1000 miles. Dividing both sides by 1 inch, we get: x = 1000 miles.

Question 9

9. A recipe calls for 2 tablespoons of sugar to make 8 cookies. How many tablespoons of sugar are needed to make 24 cookies?

Answer 9

6 tablespoons of sugar are needed. Explanation: If 2 tablespoons of sugar are needed to make 8 cookies, we can set up a proportion: 2 tablespoons / 8 cookies = x tablespoons / 24 cookies. Cross-multiplying, we get: 2 tablespoons * 24 cookies = 8 cookies * x tablespoons. Simplifying the left side: 2 * 24 = 48. So, the equation becomes: 48 = 8 * x tablespoons. Dividing both sides by 8, we get: x = 6 tablespoons.

Question 10

10. A model car is 1/32 the size of a real car. If the real car is 15 feet long, how long is the model car?

Answer 10

The model car is 5.625 inches long. Explanation: If the real car is 15 feet long and the model car is 1/32 the size, we can set up a proportion: 15 feet / 32 = x inches / 1. Simplifying the left side: 15/32 is approximately 0.47. So, the equation becomes: 0.47 = x / 1. Multiplying both sides by 1, we get: x = 0.47 inches. However, we need to convert this to inches. 1 foot is equal to 12 inches, so 15 feet is equal to 180 inches. Multiplying 0.47 by 180, we get: 0.47 * 180 = 84.6 inches. So, the model car is approximately 5.625 inches long.

Question 11

11. A map has a scale of 1 inch = 20 miles. If a city is 2.5 inches away from another city on the map, how far apart are they in real life?

Answer 11

The two cities are 50 miles apart. Explanation: If 1 inch on the map represents 20 miles in real life, we can set up a proportion: 1 inch / 20 miles = 2.5 inches / x miles. Cross-multiplying, we get: 1 inch * x miles = 2.5 inches * 20 miles. Simplifying the right side: 2.5 inches * 20 miles = 50 miles. So, the equation becomes: 1 inch * x miles = 50 miles. Dividing both sides by 1 inch, we get: x = 50 miles.

Question 12

12. A recipe calls for 1/3 cup of sugar to make 12 cookies. How many cups of sugar are needed to make 48 cookies?

Answer 12

1 and 1/3 cups of sugar are needed. Explanation: If 1/3 cup of sugar is needed to make 12 cookies, we can set up a proportion: 1/3 cup / 12 cookies = x cups / 48 cookies. Cross-multiplying, we get: 1/3 cup * 48 cookies = 12 cookies * x cups. Simplifying the left side: 1/3 * 48 = 16. So, the equation becomes: 16 = 12 * x cups. Dividing both sides by 12, we get: x = 1 and 1/3 cups.

Question 13

13. A model airplane is 1/48 the size of a real airplane. If the real airplane is 120 feet long, how long is the model airplane?

Answer 13

The model airplane is 2.5 feet long. Explanation: If the real airplane is 120 feet long and the model airplane is 1/48 the size, we can set up a proportion: 120 feet / 48 = x feet / 1. Simplifying the left side: 120/48 is equal to 2.5. So, the equation becomes: 2.5 = x / 1. Multiplying both sides by 1, we get: x = 2.5 feet.

Question 14

14. A map has a scale of 1 inch = 10 miles. If a city is 3 inches away from another city on the map, how far apart are they in real life?

Answer 14

The two cities are 30 miles apart. Explanation: If 1 inch on the map represents 10 miles in real life, we can set up a proportion: 1 inch / 10 miles = 3 inches / x miles. Cross-multiplying, we get: 1 inch * x miles = 3 inches * 10 miles. Simplifying the right side: 3 inches * 10 miles = 30 miles. So, the equation becomes: 1 inch * x miles = 30 miles. Dividing both sides by 1 inch, we get: x = 30 miles.

Question 15

15. A recipe calls for 2/3 cup of milk to make 9 pancakes. How much milk is needed to make 18 pancakes?

Answer 15

1 and 1/3 cups of milk are needed. Explanation: If 2/3 cup of milk is needed to make 9 pancakes, we can set up a proportion: 2/3 cup / 9 pancakes = x cups / 18 pancakes. Cross-multiplying, we get: 2/3 cup * 18 pancakes = 9 pancakes * x cups. Simplifying the left side: 2/3 * 18 = 12. So, the equation becomes: 12 = 9 * x cups. Dividing both sides by 9, we get: x = 4/3 cups, which is equivalent to 1 and 1/3 cups.

Question 16

16. A blueprint for a house has a scale of 1 inch = 6 feet. If the blueprint shows a room that is 10 inches wide, how wide is the room in real life?

Answer 16

The room is 60 feet wide. Explanation: If 1 inch on the blueprint represents 6 feet in real life, we can set up a proportion: 1 inch / 6 feet = 10 inches / x feet. Cross-multiplying, we get: 1 inch * x feet = 10 inches * 6 feet. Simplifying the right side: 10 inches * 6 feet = 60 feet. So, the equation becomes: 1 inch * x feet = 60 feet. Dividing both sides by 1 inch, we get: x = 60 feet.

Question 17

17. A model train is 1/64 the size of a real train. If the real train is 128 feet long, how long is the model train?

Answer 17

The model train is 2 feet long. Explanation: If the real train is 128 feet long and the model train is 1/64 the size, we can set up a proportion: 128 feet / 64 = x feet / 1. Simplifying the left side: 128/64 is equal to 2. So, the equation becomes: 2 = x / 1. Multiplying both sides by 1, we get: x = 2 feet.

Question 18

18. A map has a scale of 1 inch = 30 miles. If a city is 1.5 inches away from another city on the map, how far apart are they in real life?

Answer 18

The two cities are 45 miles apart. Explanation: If 1 inch on the map represents 30 miles in real life, we can set up a proportion: 1 inch / 30 miles = 1.5 inches / x miles. Cross-multiplying, we get: 1 inch * x miles = 1.5 inches * 30 miles. Simplifying the right side: 1.5 inches * 30 miles = 45 miles. So, the equation becomes: 1 inch * x miles = 45 miles. Dividing both sides by 1 inch, we get: x = 45 miles.

Question 19

19. A recipe calls for 1/2 cup of sugar to make 6 cupcakes. How much sugar is needed to make 24 cupcakes?

Answer 19

2 cups of sugar are needed. Explanation: If 1/2 cup of sugar is needed to make 6 cupcakes, we can set up a proportion: 1/2 cup / 6 cupcakes = x cups / 24 cupcakes. Cross-multiplying, we get: 1/2 cup * 24 cupcakes = 6 cupcakes * x cups. Simplifying the left side: 1/2 * 24 = 12. So, the equation becomes: 12 = 6 * x cups. Dividing both sides by 6, we get: x = 2 cups.

Question 20

20.A rectangular swimming pool has a length of 24 feet and a width of 12 feet. A scale drawing of the pool is made using a scale of 1 inch = 3 feet. What are the dimensions of the pool on the scale drawing?

Answer 20

The scale drawing is 8 inches by 4 inches. Explanation: If 1 inch on the scale drawing represents 3 feet in real life, we can find the length and width of the pool on the scale drawing by dividing the actual length and width by 3. The length of the pool on the scale drawing is 24/3 = 8 inches, and the width of the pool on the scale drawing is 12/3 = 4 inches.

Question 21

21. A map of a city has a scale of 1 centimeter = 2 kilometers. If two points on the map are 5 centimeters apart, what is the distance between them in kilometers?

Answer 21

The distance between the two points is 10 kilometers. Explanation: If 1 centimeter on the map represents 2 kilometers in real life, we can set up a proportion: 1 centimeter / 2 kilometers = 5 centimeters / x kilometers. Cross-multiplying, we get: 1 centimeter * x kilometers = 5 centimeters * 2 kilometers. Simplifying the right side: 5 centimeters * 2 kilometers = 10 kilometers. So, the equation becomes: 1 centimeter * x kilometers = 10 kilometers. Dividing both sides by 1 centimeter, we get: x = 10 kilometers.

Question 22

22. A toy train is 1/24 the size of a real train. If the real train is 72 feet long, how long is the toy train?

Answer 22

The toy train is 3 feet long. Explanation: If the real train is 72 feet long and the toy train is 1/24 the size, we can set up a proportion: 72 feet / 24 = x feet / 1. Simplifying the left side: 72/24 is equal to 3. So, the equation becomes: 3 = x / 1. Multiplying both sides by 1, we get: x = 3 feet.

Question 23

23. A recipe calls for 3/4 cup of flour to make 8 biscuits. How much flour is needed to make 16 biscuits?

Answer 23

1 and 1/2 cups of flour are needed. Explanation: If 3/4 cup of flour is needed to make 8 biscuits, we can set up a proportion: 3/4 cup / 8 biscuits = x cups / 16 biscuits. Cross-multiplying, we get: 3/4 cup * 16 biscuits = 8 biscuits * x cups. Simplifying the left side: 3/4 * 16 = 12. So, the equation becomes: 12 = 8 * x cups. Dividing both sides by 8, we get: x = 3/2 cups, which is equivalent to 1 and 1/2 cups.

Question 24

24. A blueprint for a house has a scale of 1 inch = 8 feet. If the blueprint shows a room that is 9 inches wide, how wide is the room in real life?

Answer 24

The room is 72 feet wide. Explanation: If 1 inch on the blueprint represents 8 feet in real life, we can set up a proportion: 1 inch / 8 feet = 9 inches / x feet. Cross-multiplying, we get: 1 inch * x feet = 9 inches * 8 feet. Simplifying the right side: 9 inches * 8 feet = 72 feet. So, the equation becomes 1 inch * x feet = 72 feet. Dividing both sides by 1 inch, we get: x = 72 feet.

Question 25

25. A map of a nature reserve has a scale of 1 inch = 2 miles. If a trail on the map is 4 inches long, how long is the actual trail?

Answer 25

The actual trail is 8 miles long. Explanation: If 1 inch on the map represents 2 miles in real life, we can set up a proportion: 1 inch / 2 miles = 4 inches / x miles. Cross-multiplying, we get: 1 inch * x miles = 4 inches * 2 miles. Simplifying the right side: 4 inches * 2 miles = 8 miles. So, the equation becomes: 1 inch * x miles = 8 miles. Dividing both sides by 1 inch, we get: x = 8 miles.

Question 26

26. A blueprint for a new office building has a scale of 1/4 inch = 3 feet. If a conference room on the blueprint is 2 inches wide, how wide is the room in real life?

Answer 26

The room is 24 feet wide. Explanation: If 1/4 inch on the blueprint represents 3 feet in real life, we can set up a proportion: 1/4 inch / 3 feet = 2 inches / x feet. Cross-multiplying, we get: 1/4 inch * x feet = 2 inches * 3 feet. Simplifying the right side: 2 inches * 3 feet = 6 feet. So, the equation becomes: 1/4 inch * x feet = 6 feet. Multiplying both sides by 4, we get: 1 inch * x feet = 24 feet. Dividing both sides by 1 inch, we get: x = 24 feet.

Question 27

27. A 1:50 scale model car is 4 inches long. How long is the real car?

Answer 27

The real car is 16.67 feet long. Explanation: If the model car is 1/50 the size of the real car, we can set up a proportion: 1/50 = 4 inches / x feet. Cross-multiplying, we get: 1 * x feet = 50 * 4 inches. Simplifying the right side: 50 * 4 inches = 200 inches. Converting inches to feet by dividing by 12, we get: 200 inches / 12 = 16.67 feet. So, the equation becomes: 1 * x feet = 16.67 feet. Dividing both sides by 1, we get: x = 16.67 feet.

Question 28

28. A map of a park has a scale of 1 centimeter = 100 meters. If a playground on the map is 4 centimeters away from a picnic area, how far apart are the actual locations?

Answer 28

The actual locations are 400 meters apart. Explanation: If 1 centimeter on the map represents 100 meters in real life, we can set up a proportion: 1 centimeter / 100 meters = 4 centimeters / x meters. Cross-multiplying, we get: 1 centimeter * x meters = 4 centimeters * 100 meters. Simplifying the right side: 4 centimeters * 100 meters = 400 meters. So, the equation becomes: 1 centimeter * x meters = 400 meters. Dividing both sides by 1 centimeter, we get: x = 400 meters.