Stable High School has a total of 112 boys and girls who play sports. If the number of boys, b is 16 more than twice the number of girls, g, how many boys play sports at this high school?

Aug 5, 2016

80 boys play sport.

Explanation:

$b = \text{number of boys" and g = "number of girls}$

There are 112 students altogether.

$b + g = 112$

This can also be written as
$b = 112 - g \text{ or as " g = 112 -b}$

It is very useful to have variables as the subject of the equation when working with simultaneous equations. This allows for easy substituting or equating.

A common mistake is to add to the boys and to multiply the boys by 2. There are more boys! - do not make them even more.

$b = 2 g + 16$

There are now 2 equations.

$b = 2 g + 16 \text{ }$ and $\text{ } b = 112 - g$

$b = b$ therefore it follows:

$2 g + 16 = 112 - g$

$3 g = 112 - 16$
$3 g = 96$

$g = 32$

$b = 80$