Question

The difference of two numbers is 16. The greater number is 5 less than 4 times the smaller

number. Find the two numbers.

Answer 1

Let x = smaller number
Let y = greater number
Then we have that y = 4x − 5y − x = 16
Replace the value of y in the second equation you get 4x − 5 − x = 16
3x − 5 = 16
3x = 21
x = 7

y = 23

Answer 2

x= 23

y=7

Explanation:

x-y=16

4y-5=x

4y-5-y=16

3y-5=16 add 5 to both sides

3y=21 divide by 3 on both sides

y=7

x-7=16 substitute back in

x=23 added 7 to both sides

so x=23 and y=7

23-7=16