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.

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ranikashyab066 ranikashyab066 · Answer 1 · 2019-12-10T11:00:20+01:00

Answer:

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

Step-by-step 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

[tex]\frac{6}{5} = \frac{96}{100 - m} \\\implies 100 - m = 96 \times\frac{5}{6} = 80\\or, 100 - 80 = m\\\implies m= 20[/tex]

or, m = 20

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