Looking for 2 numbers (CNA)

The larger of two numbers is 4 less than five times the smaller. When the smaller number is subtracted from the larger, the difference is 4. Find the numbers.


Let x be the larger number.

Let y be the smaller number

The larger of two numbers is 4 less than five times the smaller.

The above sentence gives the following equation

x = 5y - 4 equation 1

When the smaller number is subtracted from the larger, the difference is 4.

The above sentence gives the following equation

x - y = 4 equation 2

In equation 1, we know what x is.

Just replace x into equation 2

5y - 4 - y = 4

4y - 4 = 4

4y - 4 + 4 = 4 + 4

4y = 8

Since 4 × 2 = 8

y = 2

x = 5 × 2 - 4

x = 10 - 4 = 6

The two numbers are 6 and 2