EDGE Math 8

Number and Geometric Relations

In this page and the succeeding pages, you will learn about how to solve word problems by applying what you already know about solutions of systems of two linear equations in two variables.

Example 1

A certain class consists of 45 grade 8 students. The number of boys is 9 more than the number of girls. How many boys and girls are there in the class?

Solution

Let $x = number of boys$ and $y = number of girls .$ Since there are 45 students in the class,

x + y = 45.

The number of boys is 9 more than the number of girls. Hence,

x = y + 9.

The word problem translates into a system of two linear equations in two variables.

{\begin{array}{l} x + y = 45 \\ x = y + 9 \end{array}

Using the second equation, substitute $y + 9$ for x in the first equation, and then solve for y.

$(y + 9) + y$	$= 45$
$2 y$	$= 45 - 9$
$2 y$	$= 36$
$y$	$= 18$

Then substitute 18 for y in $x = y + 9$ to get the value of x.

x = y + 9 = 18 + 9 = 27

The solution of the system is $(27, 18) .$

Checking

Use the conditions in the problem. The number of boys and the number of girls add up to $27 + 18 = 45.$
Moreover, the number of boys (which is 27) is 9 more than the number of girls (which is 18). The conditions of the given problem are satisfied. Hence, there are 27 boys and 18 girls in the class.