Question

One number is 24 more than the other. What are the numbers if their sum is 84

Answer 1

The required numbers are 30 and 54.

Explanation:

• Let 'x' be the smaller number

• Let 'y' be the larger number

Given that one number is 24 more than the other, so

`y = x + 24`

Given that the sum of the numbers is 84, so

`x + y = 84`

so we have two equations

`\begin{bmatrix}y=x+24\\ x+y=84\end{bmatrix}`

Arrange equation variables for elimination

`\begin{bmatrix}y-x=24\\ y+x=84\end{bmatrix}`

subtracting the equartions

`y+x=84`

`-`

`\underline{y-x=24}`

`2x=60`

now solve 2x = 60 for x

`2x=60`

Divide both sides by 2

`(2x)/(2)=(60)/(2)`

Simplify

`x=30`

For y - x = 24 plug in x = 30

`y-30=24`

Add 30 to both sides

`y-30+30=24+30`

Simplify

`y=54`

Thus, the required numbers are 30 and 54.

Verification:

Given that one number is 24 more than the other, so

`y = x + 24`

substitute x = 30

y = 30 + 24

y = 54

Thus, y is 24 more than x.

Given that the sum of the numbers is 84, so

`x + y = 84`

sustitute x = 30 and y = 54

30 + 54 = 84

84 = 84

L.H.S = R.H.S

Thus, the sum of the numbers is indeed 84.