Chapter 6.2, Problem 21P

The population of a city is 2,500. If the number of males is 240 more than the number of females, how many males and females are there in the city?

To determine

To find: Number of males and females in the city.

Answer to Problem 21P

The number of male is 1370 and the number of female is 1130.

Explanation of Solution

Given information:

The population of a city is 2,500. The number of males is 240 more than the number of females.

Calculation:

The population of a city is 2,500. The number of males is 240 more than the number of females.

Let us assume the number of male is x and the number of female is y.

Hence we can write the above statement in equation form as follows:

  $\begin{array}{l}x+y=2500\\ x-y=240\end{array}$

In order to solve two systems by substitution, we solve one of the equations for one of the variables, and plug this into other equation.

  $\begin{array}{l}x+y=2500\\ x-y=240\end{array}$

As it is given that

  $\begin{array}{l}x-y=240\\ \Rightarrow x=240+y\end{array}$

Now we substitute $x=240+y$ into $x+y=2500$ , we get,

  $\begin{array}{l}x+y=2500\\ \Rightarrow 240+y+y=2500\\ \Rightarrow 2y=2260\\ \Rightarrow y=1130\end{array}$

By plugging $y=1130$ in equation $x=240+y$ we get

  $\begin{array}{l}x=240+y\\ \Rightarrow x=20+1130\\ \Rightarrow x=1370\end{array}$

Therefore the solution is

  $\left(x,y\right)=(1370,1130)$

Therefore, the number of male is 1370 and the number of female is 1130.