Question

A collector has 70 movie posters and 60 band posters. She wants to sell 42 movie posters but still have her poster collection maintain the same ratio of 70:60. If she sells 42 movie posters, how many band posters should she sell?

Answer 1

To maintain the ratio of movie posters to band posters, the collector should sell approximately 150 band posters.

Step-by-step explanation:

To maintain the same ratio of movie posters to band posters, we need to determine the number of band posters she should sell.

Step 1: Calculate the ratio of movie posters to band posters before selling any posters:
Movie posters : Band posters = 70:60

Step 2: Calculate the ratio of movie posters to band posters after selling 42 movie posters:
Movie posters : Band posters = (70-42) : x

Step 3: Set up and solve a proportion to find x:
(70-42)/60 = 70/x

Step 4: Simplify and solve for x:
28/60 = 70/x

Step 5: Cross-multiply and solve for x:
28x = 60 * 70

Step 6: Divide both sides by 28 to solve for x:
x = (60 * 70)/28

Therefore, the collector should sell approximately 150 band posters to maintain the same ratio of 70:60 after selling 42 movie posters.