Question

The sum of three numbers is 54. The third number is 6 more than the first. The second number is 2 times the third. What are the numbers?

Answer 1

9, 30, and 15.

Explanation:

Let the three numbers be a, b, and c.

The sum of them is 54. So:

`a+b+c=54`

The third number is 6 more than the first. In other words, c=a+6.

The second number is twice the third. In other words, b=2c.

Let’s write the second number in terms of a. Since b=2c, this means that b=2(a+6).

Let’s substitute them into our equation. So:

`a+2(a+6)+(a+6)=54`

Solve for a. Distribute:

`a+2a+12+a+6=54`

Combine like terms:

`4a+18=54`

Subtract 18 from both sides:

`4a=36`

Hence, the value of a is:

`a=9`

So, the first number is 9.

The third number is 6 more than the first, so the third number is 15.

The second number is twice the third. So, the second number is 30.

Therefore, our numbers are:

9, 30, and 15.