Question

The sum of three numbers is 72 the second number is three times the third the third number is eight more than the first what are the numbers

Answer 1

Our three numbers are 8, 48, and 16.

Explanation:

Let the first, second, and third numbers be x, y, and z, respectively.

The sum of them is 72. In other words:

`x + y + z = 72`

The second number y is three times the third number z. So:

`y = 3z`

And the third number z is eight more than the first number x. So:

`z = x + 8`

To find the numbers, solve for the system. We can substitute the last two equations into the first:

`x + (3z) + ( x + 8) = 72`

Substitute again:

`\displaystyle x + 3(x+8) + x+8 = 72`

Solve for x. Distribute:

`x+3x+24+x+8=72`

Combine like term:

`5x + 32 = 72`

Subtract:

`5x = 40`

And divide:

`x=8`

Thus, the first number is eight.

And since the third number is eight more than the first, the third number z is 16.

The second number is three times the third. Thus, the second number y is 3(16) or 48.

Our three numbers are 8, 48, and 16.