Question

One number is two less than seven times another number. If the sum of the numbers is 22, find the numbers.

Answer 1

19 and 3

Explanation:

Given

Let both numbers be a and b.

So:

`a + b = 22` --- Their sum

`a = 7b-2` --- 2 less than 7 of the other number

Required

Find both numbers

`a + b = 22`

`a = 7b-2`

Substitute 7b - 2 for a in the first equation

`7b - 2 + b = 22`

Collect like terms

`7b + b = 22 + 2`

`8b = 24`

Divide both sides by 8

`(8b)/(8) = (24)/(8)`

`b = (24)/(8)`

`b = 3`

Substitute 3 for b in
`a = 7b-2`

`a = 7 * 3 - 2`

`a = 21 - 2`

`a = 19`

Hence, the numbers are 19 and 3