Question

In the following exercises, translate to a system of equations and solve.

The sum of two numbers is 30. One number is 4 less than the other. Find the numbers.

Short answer

The numbers are 13 and 17

Step-by-step solution

Step 1. Given Information 

The given data is that the sum of two numbers is 30. One number is 4 less than the other.

Step 2. Calculation 

Let us assume that x be the first number and y be the second number.

The sum of two number is 30 implies that $x+y=30--\left(1\right)$

One number is 4 less than the other implies that $x=y-4--\left(2\right)$

Substitute the value of variable x from equation (2) in equation (1).

localid="1647450236787" $$\begin{gathered} x+y=30 \\ y-4+y=30 \\ 2y=34 \\ y=17 \end{gathered}$$

Find the value of variable x by using the obtained value of y.

$$\begin{gathered} x=y-4 \\ x=17-4 \\ x=13 \end{gathered}$$

Thus, the required ordered pair is$(13,17)$