Question

A collector has 120 movie posters and 100 band posters. She wants

to sell 24 movie posters but still have her poster collection maintain
the same ratio of 120:100. If she sells 24 movie posters, how many band
posters should she sell? Explain.

Answer 1

She should sell 20 band posters from total 80 to keep the maintain the same ratio.

Explanation:

The total number of movie posters collector has = 120

The total number of band posters collector has = 80

The current ratio of movie poster : band poster = 120 : 100

or, reducing the ratio further, we get

ratio of movie poster : band poster = 6 : 5 ...... (1)

Now, the number of posters she wants to sell = 24

So, the remaining movie poster left = 120 - 24 = 96

Let us assume she sells m band posters to keep the ratio equal.

So, the number of band posters she is left with = 100 - m

⇒The ratio of movie poster left : band poster left = 96 : 100 - m .. (2)

Now here as the ratio remains same after selling m band posters, so

`(6)/(5)  = (96)/(100 - m) \\\implies 100 - m = 96 *(5)/(6) =  80\\or, 100 - 80 = m\\\implies  m= 20`

or, m = 20

Hence, she should sell 20 band posters from total 80 to keep the maintain the same ratio.