# The sum of three numbers is 137. The second number is four more than, two times the first number. The third number is five less than, three times the first number. How do you find the three numbers?

Jun 20, 2016

The numbers are 23, 50 and 64.

#### Explanation:

Start by writing an expression for each of the three numbers. They are all formed from the first number, so let's call the first number $x$.

Let the first number be $x$
The second number is $2 x + 4$
The third number is $3 x - 5$

We are told that their sum is 137. This means when we add them all together the answer will be 137.
Write an equation.

$\left(x\right) + \left(2 x + 4\right) + \left(3 x - 5\right) = 137$

The brackets are not necessary, they are included for clarity.

$6 x - 1 = 137$
$6 x = 138$
$x = 23$

As soon as we know the first number, we can work out the other two from the expressions we wrote at the beginning.

$2 x + 4 = 2 \times 23 + 4 = 50$
$3 x - 5 = 3 \times 23 - 5 = 64$

Check: $23 + 50 + 64 = 137$