Question

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

Answer 1

Answer:

111 girls

Step-by-step 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:

$\frac{20}{17}$

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

$\frac{x}{85}$

Equate both fractions

$\frac{20}{17} = \frac{x}{85}$

Multiply both sides by 85

$85 * \frac{20}{17} = \frac{x}{85} * 85$

$85 * \frac{20}{17} = x$

$\frac{1700}{17} = x$

$100 = x$

$x = 100$

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;

$Outdoor = \frac{3}{3 + 2} * Total$

$Outdoor = \frac{3}{3 + 2} * 185$

$Outdoor = \frac{3}{5} * 185$

$Outdoor = \frac{555}{5}$

$Outdoor = 111$

Hence, the number of girls that chose outdoor is 111