Question

At the beginning of the school year dance, the ratio of the number of boys to the number of girls was 3:7 , if there were 100 more girls than boys, how many boys were at the dance? €¦. How many girls were at the dance?

Answer 1

boys (b): b

girls (g): b + 100

total (T) = b + g

I am going to set up the proportion as "boys" to "total"

   $\frac{3}{10} = \frac{b}{(b) + (b + 100)}$

⇒ $\frac{3}{10} = \frac{b}{2b + 100}$

⇒ 3(2b + 100) = 10(b)

⇒ 6b + 300 = 10b

⇒          300 = 4b

⇒            75 = b

girls (g): b + 100   = (75) + 100   = 175

Answer: boys = 75, girls = 175