Question

The sum of three numbers is 97. The third number is 3 times the second. The second number is 8 more than the first. What are the numbers? A) First number: B) Second number: C) Third number:

Answer 1

A) First number: 13

B) Second number: 21

C) Third number: 63

Explanation:

Let x, y and z be 1st, 2nd and 3rd numbers respectively.

We have been given that sum of three numbers is 97. We can represent this information in an equation as:

`x+y+z=97...(1)`

The 3rd number is 3 times the second. We can represent this information in an equation as:

`z=3y...(2)`

The second number is 8 more than the first. We can represent this information in an equation as:

`y=x+8...(3)`

Substituting equation (3) in equation (2), we will get:

`z=3(x+8)`

Substituting
`z=3(x+8)` and
`y=x+8` in equation (1), we will get:

`x+x+8+3(x+8)=97`

`x+x+8+3x+24=97`

`5x+32=97`

`5x+32-32=97-32`

`5x=65`

`(5x)/(5)=(65)/(5)`

`x=13`

Therefore, the first number is 13.

Now, we will substitute
`x=13` in equation (3) as:

`y=21`

Therefore, the second number is 21.

Now, we will substitute
`y=21` in equation (2) as:

`z=3(21)`

`z=63`

Therefore, the third number is 63.