A collector has 100 movie posters and 80 band posters. She wants to sell 30 movie posters but still have her poster collection maintain the same ratio of 100:80. If she sells 30 movie posters, how many band posters should she sell? Complete the explanation to find out how many band posters she should sell.

24 band posters should be sold

Step-by-step explanation:

First take the expression down to its simplest form;

= 5:4

Assume she sells 30 movie posters, her movies posters drop to;

= 100 - 30

= 70 movie posters

We need a number of band posters remaining that will give a ratio of 5:4 with movie posters.

In fraction form, the number of movie posters is;

= 5/9 because 9 would be the total number of both movie posters and band posters.

Create an expression to find the total number of posters if 70 are movie posters;

5/9x = 70

x = 70 ÷ 5/9

x = 126 posters

Number of band posters that should be left are;

= 126 - 70

= 56

Number of band posters that should be sold;

= 80 - 56

= 24 posters

The new ratio would be 70:56.

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.