Question

Students surveyed boys and girls separately to determine whether they wanted outdoor

recess or indoor recess. After completing the boy survey, it was determined that for
every 17 boys who wanted outdoor, 20 boys wanted indoor. The girl survey had a ratio of
3:2 of outdoor to indoor. If the same number of boys and girls were surveyed, and 85
boys chose outdoor, how many girls do you think chose outdoor?

Answer 1

111 girls

Explanation:

Given

Boys: Every 17 outdoor ≈ 20 indoor

Girls: 3:2 outdoor to indoor

First, we'll determine the ratio of outdoor to indoor for boys;

Recall that;

17 choose indoor while 20 choose outdoor;

The ratio of outdoor to indoor is;

20 : 17

Convert to fraction:

`(20)/(17)`

Let x represent number of boys that choose indoor when 85 boys chose outdoor;

The ratio of outdoor to indoor is;

x : 85

Convert to fraction

`(x)/(85)`

Equate both fractions

`(20)/(17) = (x)/(85)`

Multiply both sides by 85

`85 * (20)/(17) = (x)/(85) * 85`

`85 * (20)/(17) = x`

`(1700)/(17) = x`

`100 = x`

`x = 100`

This implies that when 85 chose outdoor, 100 chose indoor for boys;

Total = 100 + 85

Total = 185 boys surveyed

Recall that the question says the same number of boys and girls were surveyed

This implies that

Total Girls Surveyed = 185

For the girl ratio;

Outdoor to Indoor= 3:2

Number of girls that chose outdoor is as follows;

`Outdoor = (3)/(3 + 2) * Total`

`Outdoor = (3)/(3 + 2) * 185`

`Outdoor = (3)/(5) * 185`

`Outdoor = (555)/(5)`

`Outdoor = 111`

Hence, the number of girls that chose outdoor is 111