Question

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

Answer 1

Answer:

The required numbers are 30 and 54.

Step-by-step 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

$\frac{2x}{2}=\frac{60}{2}$

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.