A collector has 120 movie posters and 80 band posters. She wants to sell 24 movie posters but still have her poster collection maintain the same ratio of 120:80. If she sells 24 movie posters, how many band posters should she sell? Complete the explanation to find out how many band posters she should sell. (I need help with finding the band posters. I'm stuck on 120/80 = 96/____)
To find out how many band posters she should sell, we first need to calculate the ratio of movie posters to band posters after selling 24 movie posters.
The initial ratio of movie posters to band posters is 120:80, which can be simplified as 3:2 by dividing both numbers by 40.
If the collector sells 24 movie posters, she will be left with 120 - 24 = 96 movie posters.
To maintain the same ratio, we need to find the corresponding number of band posters.
We can set up a proportion using the known ratios:
3/2 = 96/x
We cross-multiply and solve for x:
3x = 2 * 96
3x = 192
x = 192 / 3
x ≈ 64
Therefore, she should sell 64 band posters to maintain the same ratio of 120:80 after selling 24 movie posters.