# Nick is three years young than Sam. The sum of their ages is 33. How old are they?

Apr 14, 2018

Sam: 18
NIck: 15

#### Explanation:

Let Nick's age be x and let Sam's age be y.
Translate the sentence into 2 equations to get a system of equations:
$x = y - 3$
$x + y = 33$

There are several ways to solve a system of linear equations. "Substitution" is one of those methods:

Since $x = y - 3$ is solve for x, we will replace the $x$ in the second equation with $y - 3$.

$x + y = 33$

$\left(y - 3\right) + y = 33 \text{ }$ Now, solve for y

$2 y - 3 = 33$

$2 y = 36$

$y = 18 \text{ }$ Once we have y, we can substitute y back into one of the original equations to find x.

$x = y - 3$

$x = \left(18\right) - 3$

$x = 15$