Question

At Tomi's middle school, $40\%$ of the students are boys. Fifty percent of the boys chose blue as their favorite color, while $20\%$ of the girl students chose blue as their favorite color. Of the students who chose blue as their favorite color, what fraction are boys? Express your answer as a common fraction.

Answer 1

Answer:

$\frac{5}{8}$

Step-by-step explanation:

Let the total number of students = x,

∴ Number of boys = 40% of x = 0.4x,

So, the number of girls = students - boys

= x - 0.4x

= 0.6x

Now, 50% of the boys chosen blue as their favourite colour,

So, the number of boys whose favourite colour is blue = 50% of 0.4x

= 0.50 × 0.4x

= 0.2x,

Now, 20% of the girls chosen blue as their favourite colour,

So, the number of girls whose favourite colour is blue = 20% of 0.6x

= 0.20 × 0.6x

= 0.12x

Thus, the total students who like blue colour = 0.20x + 0.12x = 0.32x

Also, the fraction of the boys whose favourite colour is blue out of the total students who like blue

$=\frac{0.2x}{0.32x}$

$=\frac{5}{8}$