Question

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?

Answer 1

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 = 2b`

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 = 2b - 8`

Add `8` to both ends to get:

`b + 8 = 2b`

Subtract `b` from both sides to get:

`b = 8`

Then substitute this value into the first equation:

`g = 2b = 2xx8 = 16`