2 Scale To Amount Set 1

Question 1

29 . A blueprint for a new shopping mall has a scale of 1/8 inch = 1 foot. If a store on the blueprint is 3 inches wide, how wide is the store in real life?

Answer 1

The store is 24 feet wide.
Explanation:
If 1/8 inch on the blueprint represents 1 foot in real life, we can set up a proportion: 1/8 inch / 1 foot = 3 inches / x feet. Cross-multiplying, we get: 1/8 inch * x feet = 3 inches * 1 foot. Simplifying the right side: 3 inches * 1 foot = 3 feet. So, the equation becomes: 1/8 inch * x feet = 3 feet. Multiplying both sides by 8, we get: 1 inch * x feet = 24 feet. Dividing both sides by 1 inch, we get: x = 24 feet.

Question 2

30. A 1:75 scale model airplane has a wingspan of 8 inches. How wide is the wingspan of the real airplane?

Answer 2

The wingspan of the real airplane is 50 feet.
Explanation:
If the model airplane is 1/75 the size of the real airplane, we can set up a proportion: 1/75 = 8 inches / x feet. Cross-multiplying, we get: 1 * x feet = 75 * 8 inches. Simplifying the right side: 75 * 8 inches = 600 inches. Converting inches to feet by dividing by 12, we get: 600 inches / 12 = 50 feet. So, the equation becomes: 1 * x feet = 50 feet. Dividing both sides by 1, we get: x = 50 feet.

Question 3

31. A map of a city has a scale of 1 inch = 2 miles. If a park on the map is 3 inches away from a library, how far apart are the actual locations?

Answer 3

The actual locations are 6 miles apart.
Explanation:
If 1 inch on the map represents 2 miles in real life, we can set up a proportion: 1 inch / 2 miles = 3 inches / x miles. Cross-multiplying, we get: 1 inch * x miles = 3 inches * 2 miles. Simplifying the right side: 3 inches * 2 miles = 6 miles. So, the equation becomes: 1 inch * x miles = 6 miles. Dividing both sides by 1 inch, we get: x = 6 miles.

Question 4

32. A blueprint for a new school has a scale of 1/4 inch = 1 foot. If a classroom on the blueprint is 2 inches wide, how wide is the classroom in real life?

Answer 4

The classroom is 8 feet wide.
Explanation:
If 1/4 inch on the blueprint represents 1 foot in real life, we can set up a proportion: 1/4 inch / 1 foot = 2 inches / x feet. Cross-multiplying, we get: 1/4 inch * x feet = 2 inches * 1 foot. Simplifying the right side: 2 inches * 1 foot = 2 feet. So, the equation becomes: 1/4 inch * x feet = 2 feet. Multiplying both sides by 4, we get: 1 inch * x feet = 8 feet. Dividing both sides by 1 inch, we get: x = 8 feet.

Question 5

33. A 1:100 scale model train has a length of 10 inches. How long is the real train?

Answer 5

The real train is 83.33 feet long.
Explanation:
If the model train is 1/100 the size of the real train, we can set up a proportion: 1/100 = 10 inches / x feet. Cross-multiplying, we get: 1 * x feet = 100 * 10 inches. Simplifying the right side: 100 * 10 inches = 1000 inches. Converting inches to feet by dividing by 12, we get: 1000 inches / 12 = 83.33 feet (rounded to two decimal places). So, the equation becomes: 1 * x feet = 83.33 feet. Dividing both sides by 1, we get: x = 83.33 feet.

Question 6

34. A map of a town has a scale of 1 inch = 1 mile. If a park on the map is 2.5 inches away from a school, how far apart are the actual locations?

Answer 6

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

Question 7

35. A blueprint for a new office building has a scale of 1/2 inch = 10 feet. If a conference room on the blueprint is 3.5 inches long, how long is the conference room in real life?

Answer 7

The conference room is 70 feet long.
Explanation:
If 1/2 inch on the blueprint represents 10 feet in real life, we can set up a proportion: 1/2 inch / 10 feet = 3.5 inches / x feet. Cross-multiplying, we get: 1/2 inch * x feet = 3.5 inches * 10 feet. Simplifying the right side: 3.5 inches * 10 feet = 35 feet. So, the equation becomes: 1/2 inch * x feet = 35 feet. Multiplying both sides by 2, we get: 1 inch * x feet = 70 feet. Dividing both sides by 1 inch, we get: x = 70 feet.

Question 8

36. A 1:50 scale model car has a length of 4 inches. How long is the real car?

Answer 8

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 (rounded to two decimal places). So, the equation becomes: 1 * x feet = 16.67 feet. Dividing both sides by 1, we get: x = 16.67 feet.

Question 9

37. A map of a city has a scale of 1 inch = 5 miles. If a park on the map is 4 inches away from a museum, how far apart are the actual locations?

Answer 9

The actual locations are 20 miles apart.
Explanation:
If 1 inch on the map represents 5 miles in real life, we can set up a proportion: 1 inch / 5 miles = 4 inches / x miles. Cross-multiplying, we get: 1 inch * x miles = 4 inches * 5 miles. Simplifying the right side: 4 inches * 5 miles = 20 miles. So, the equation becomes: 1 inch * x miles = 20 miles. Dividing both sides by 1 inch, we get: x = 20 miles.

Question 10

38. A blueprint for a new house has a scale of 1/4 inch = 1 foot. If a bedroom on the blueprint is 2 inches long, how long is the bedroom in real life?

Answer 10

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

Question 11

39. A 1:100 scale model airplane has a wingspan of 12 inches. What is the wingspan of the real airplane?

Answer 11

The wingspan of the real airplane is 100 feet.
Explanation:
If the model airplane is 1/100 the size of the real airplane, we can set up a proportion: 1/100 = 12 inches / x feet. Cross-multiplying, we get: 1 * x feet = 100 * 12 inches. Simplifying the right side: 100 * 12 inches = 1200 inches. Converting inches to feet by dividing by 12, we get: 1200 inches / 12 = 100 feet. So, the equation becomes: 1 * x feet = 100 feet. Dividing both sides by 1, we get: x = 100 feet.

Question 12

40. A map of a park has a scale of 1 inch = 2 kilometers. If a lake on the map is 3 inches away from a trail, how far apart are the actual locations?

Answer 12

The actual locations are 6 kilometers apart.
Explanation:
If 1 inch on the map represents 2 kilometers in real life, we can set up a proportion: 1 inch / 2 kilometers = 3 inches / x kilometers. Cross-multiplying, we get: 1 inch * x kilometers = 2 kilometers * 3 inches. Simplifying the right side: 2 kilometers * 3 inches = 6 kilometers. So, the equation becomes: 1 inch * x kilometers = 6 kilometers. Dividing both sides by 1 inch, we get: x = 6 kilometers. 41. A model of a car has a scale of 1:24. If the model car is 6 inches long, how long is the actual car?

Question 13

42. A drawing of a city block has a scale of 1/2 inch = 200 feet. If a building on the drawing is 1 inch wide, how wide is the building in real life?

Answer 13

The building is 400 feet wide.
Explanation:
If 1/2 inch on the drawing represents 200 feet in real life, we can set up a proportion: 1/2 inch / 200 feet = 1 inch / x feet. Cross-multiplying, we get: 1/2 inch * x feet = 200 feet * 1 inch. Simplifying the right side: 200 feet * 1 inch = 200 feet. So, the equation becomes: 1/2 inch * x feet = 200 feet. Multiplying both sides by 2, we get: 1 inch * x feet = 400 feet. Dividing both sides by 1 inch, we get: x = 400 feet.

Question 14

43. A map of a hiking trail has a scale of 1 inch = 2 miles. If the trail is 12 inches long on the map, how long is the actual trail?

Answer 14

The actual trail is 24 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 = 12 inches / x miles. Cross-multiplying, we get: 1 inch * x miles = 2 miles * 12 inches. Simplifying the right side: 2 miles * 12 inches = 24 miles. So, the equation becomes: 1 inch * x miles = 24 miles. Dividing both sides by 1 inch, we get: x = 24 miles.

Question 15

44. A blueprint for a new office building has a scale of 1/8 inch = 1 foot. If a conference room on the blueprint is 3 inches long, how long is the conference room in real life?

Answer 15

The conference room is 24 feet long.
Explanation:
If 1/8 inch on the blueprint represents 1 foot in real life, we can set up a proportion: 1/8 inch / 1 foot = 3 inches / x feet. Cross-multiplying, we get: 1/8 inch * x feet = 3 inches * 1 foot. Simplifying the right side: 3 inches * 1 foot = 3 feet. So, the equation becomes: 1/8 inch * x feet = 3 feet. Multiplying both sides by 8, we get: 1 inch * x feet = 24 feet. Dividing both sides by 1 inch, we get: x = 24 feet.

Question 16

45. A model of a train has a scale of 1:48. If the model train is 10 inches long, how long is the actual train?

Answer 16

The actual train is 40 feet long.
Explanation:
If the model train is 1/48 the size of the actual train, we can set up a proportion: 1/48 = 10 inches / x feet. Cross-multiplying, we get: 1 * x feet = 48 * 10 inches. Simplifying the right side: 48 * 10 inches = 480 inches. Converting inches to feet by dividing by 12, we get: 480 inches / 12 = 40 feet. So, the equation becomes: 1 * x feet = 40 feet. Dividing both sides by 1, we get: x = 40 feet.

Question 17

46. A model of a ship has a scale of 1:120. If the model ship is 16 inches long, how long is the actual ship?

Answer 17

The actual ship is 160 feet long.
Explanation:
If the model ship is 1/120 the size of the actual ship, we can set up a proportion: 1/120 = 16 inches / x feet. Cross-multiplying, we get: 1 * x feet = 120 * 16 inches. Simplifying the right side: 120 * 16 inches = 1920 inches. Converting inches to feet by dividing by 12, we get: 1920 inches / 12 = 160 feet. So, the equation becomes: 1 * x feet = 160 feet. Dividing both sides by 1, we get: x = 160 feet.

Question 18

47. A map of a state has a scale of 1 inch = 50 miles. If a city on the map is 2.5 inches from another city, how far apart are the cities in real life?

Answer 18

The cities are 125 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 = 2.5 inches / x miles. Cross-multiplying, we get: 1 inch * x miles = 50 miles * 2.5 inches. Simplifying the right side: 50 miles * 2.5 inches = 125 miles. So, the equation becomes: 1 inch * x miles = 125 miles. Dividing both sides by 1 inch, we get: x = 125 miles.

Question 19

48. A blueprint for a new house has a scale of 1/4 inch = 1 foot. If a bedroom on the blueprint is 2 inches wide, how wide is the bedroom in real life?

Answer 19

The bedroom is 8 feet wide.
Explanation:
If 1/4 inch on the blueprint represents 1 foot in real life, we can set up a proportion: 1/4 inch / 1 foot = 2 inches / x feet. Cross-multiplying, we get: 1/4 inch * x feet = 2 inches * 1 foot. Simplifying the right side: 2 inches * 1 foot = 2 feet. So, the equation becomes: 1/4 inch * x feet = 2 feet. Multiplying both sides by 4, we get: 1 inch * x feet = 8 feet. Dividing both sides by 1 inch, we get: x = 8 feet.

Question 20

49. A model of a plane has a scale of 1:96. If the model plane is 8 inches long, how long is the actual plane?

Answer 20

The actual plane is 64 feet long.
Explanation:
If the model plane is 1/96 the size of the actual plane, we can set up a proportion: 1/96 = 8 inches / x feet. Cross-multiplying, we get: 1 * x feet = 96 * 8 inches. Simplifying the right side: 96 * 8 inches = 768 inches. Converting inches to feet by dividing by 12, we get: 768 inches / 12 = 64 feet. So, the equation becomes: 1 * x feet = 64 feet. Dividing both sides by 1, we get: x = 64 feet.

Question 21

50. A blueprint for a new building has a scale of 1/8 inch = 1 foot. If a hallway on the blueprint is 3 inches wide, how wide is the hallway in real life?

Answer 21

The hallway is 24 feet wide.
Explanation:
If 1/8 inch on the blueprint represents 1 foot in real life, we can set up a proportion: 1/8 inch / 1 foot = 3 inches / x feet. Cross-multiplying, we get: 1/8 inch * x feet = 3 inches * 1 foot. Simplifying the right side: 3 inches * 1 foot = 3 feet. So, the equation becomes: 1/8 inch * x feet = 3 feet. Multiplying both sides by 8, we get: 1 inch * x feet = 24 feet. Dividing both sides by 1 inch, we get: x = 24 feet.