Question

The difference of two numbers is 5. The sum of three times the larger number and twice the smaller number is 30. What is the smaller

number?

A. 1
B. 2
C. 3
D. 4
E. 5​

Answer 1

C. 3

Explanation:

Let the larger number be denoted by x.

Let the smaller number be denoted by y.

Given the following parameters;

`x - y = 5` ............equation 1

`3x + 2y = 30` .........equation 2

From equation 1;

`x = 5 + y` .........equation 3

Substituting equation 3 into equation 2, we have;

`3(5+y) + 2y = 30`

`15 + 3y + 2y = 30`

`15 + 5y = 30`

`5y = 30 - 15`

5y = 15

Divide both sides by 5;

y = 15/5

y = 3.

Substituting the value of y into equation 3, we have;

`x = 5 + y`

x = 5 + 3 = 8.

Therefore, the value of the smaller number is 3 and the larger number is 8.