Question

The sum of two numbers is 100. The sum of 8 and the larger number is equal to 5 times the smaller number. What is the smaller number?

Answer 1

The smaller number is 18.

Explanation:

We have given that

The sum of two numbers is 100. The sum of 8 and the larger number is equal to 5 times the smaller number.

Let x and y are two numbers.

Let y is the larger number.

x+y = 100 eq(1)

y+8 = 5x eq(2)

From eq(1), we have

y = 100-x

Putting above eq(3) into eq(2), we have

100-x+8 = 5x

108 = 5x+x

108 = 6x

x = 108/6

x = 18

Hence, the smaller number is 18.

Answer 2

The smaller number is 18

Explanation:

Let the numbers be
`x` and
`y` where x is the smaller number;
`y\:>\:x`.

The sum of the numbers is 100.

`x+y=100...(1)`

The sum of 8 and the larger number is equal to 5 times the smaller number.

`y+8=5x`

`\Rightarrow y=5x-8...(2)`

Put equation (2) into equation (1).

`x+5x-8=100`

`x+5x=100+8`

`6x=108`

`x=18`