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 the collector should sell, we can use the information given to set up a proportion.
The ratio of movie posters to band posters is given as 120:80. If the collector sells 24 movie posters, then she will have 120 - 24 = 96 movie posters remaining.
Let "x" represent the number of band posters she should sell.
The new ratio can be represented as (96 - 24):x.
So, the proportion can be set up as (96 - 24) / x = 120 / 80.
To find the value of "x", we can cross-multiply and solve for the unknown:
(96 - 24) * 80 = 120 * x.
72 * 80 = 120 * x,
5760 = 120 * x,
5760 / 120 = x,
x = 48.
Therefore, the collector should sell 48 band posters in order to maintain the same ratio of 120:80.