Question

the ratio of boys to girls in grade 8 at a certain vancouver high school is 5:3.
a) the entire cohort of grade 8s has 126 girls. how many boys are there?
b) in a group of 40 grade 8 students, how many boys would you expect there to be?
c) the ratio of boys to girls in grade 9 is also 5:3, while in grade 10 the ratio of boys to girls is 5:7. if both grade 9 and 10 have 288 students each, how many more girls are there in grade 10 than in grade 9?

Explanation:

Set up the Grade 8 ratio

Using the Proportional Reasoning knowledge point

$$ \frac{\text{boys}}{\text{girls}} = \frac{5}{3} $$

Solve for Grade 8 boys

Using the Proportional Reasoning knowledge point

$$
LATEXBLOCK0
$$

Calculate expected boys in a group of 40

Using the Proportional Reasoning knowledge point

$$
LATEXBLOCK1
$$

Calculate girls in Grade 9 and Grade 10

Using the Proportional Reasoning knowledge point

$$
LATEXBLOCK2
$$

Find the difference in girls

Using the Proportional Reasoning knowledge point

$$ \text{Difference} = 168 - 108 = 60 $$

Answer:

Question a

There are 210 boys.

Question b

You would expect there to be 25 boys.

Question c

There are 60 more girls in Grade 10 than in Grade 9.