Question

One number is 4 less than a second number. Twice the second number is 16 less than 5 times the first. Find the two numbers.

Answer 1

Call the first number x and the second number y.

x = y - 4
2y = 5x - 16

Substitute what x equals from the first equation in the second equation.

2y = 5(y - 4) - 16

2y = 5y - 20 - 16

-3y = -36

y = 12

Now use the first equation for find x.

x = y - 4

x = 12 - 4

x = 8

The numbers are 8 and 12.

Let's check:

8 is 4 less than 12.

Twice 12 is 24.
5 times 8 is 40, and 16 less than 40 is 24.

Our answer is correct.