# Determine 2 consecutive integersWhat are two consecutive integers such that eight times the larger minus four times the smaller is 88?

pohnpei397 | Certified Educator

The numbers are 21 and 20.

Set up the equation like this:

y = x + 1

8y - 4x = 88

Now take the value for y in the first equation and substitute it into the second equation.

8 (x + 1) - 4x = 88

8x + 8 - 4x = 88

8x - 4x = 80

4x = 80

x = 20

Plug this value for x into the first equation.

y = 20 + 1

y = 21

The values of the two numbers are 20 and 21.

giorgiana1976 | Student

We'll note the consecutive integers as x and x + 1.

Since the enunciation contains the terms "the larger" and "the smaller", we'll identify the larger number as x+1 and the smaller as x.

We'll write mathematically the enunciation:

eight times the larger = 8(x+1)

four times the smaller = 4x

8(x+1) - 4x = 88

We'll remove the brackets:

8x + 8 - 4x = 88

We'll isolate x to the left side. For this reason, we'll subtract 8 both sides:

4x = 88 - 8

4x = 80

We'll divide by 4:

x = 20

The numbers are: x = 20 and x + 1 = 21.