# There are twice as many girls as boys in the school chorus. There are eight fewer boys than girls in the chorus. How do you write a system of equations to represent this situation and solve?

May 25, 2015

Choose symbols to stand for the various quantities described in the problem and express the described relations between those numbers in terms of the symbols you have chosen.

Let $g$ represent the number of girls in the school chorus.
Let $b$ represent the number of boys in the school chorus.

There are twice as many girls as boys in the school chorus:
$g = 2 b$

There are eight fewer boys than girls in the chorus:
$b = g - 8$

To solve, substitute for $g$ in the second equation, using the first one:

$b = g - 8 = 2 b - 8$

Add $8$ to both ends to get:

$b + 8 = 2 b$

Subtract $b$ from both sides to get:

$b = 8$

Then substitute this value into the first equation:

$g = 2 b = 2 \times 8 = 16$