# How do you find 2 number if the sum of two numbers is 22 and the first number is 10 less than 3 times the other number?

May 22, 2018

$14$ and $8$

#### Explanation:

let the two numbers be $a$ and $b$.

1) the sum of the two numbers is 22

$a + b = 22$

2) the first number is 10 less than 3 times the other number:

$a = 3 b - 10$

We can substitute the second expression into the first one to get the following expression and solve for b:

$a + b = 22 \to \left(3 b - 10\right) + b = 22$

$4 b - 10 = 22$
$4 b = 32$
$b = 8$

Now since $a + b = 22$ and $b = 8$, $a + 8 = 22$ and therefore $a = 14$

$a = 14$, $b = 8$