# On Tuesday, a local hamburger shop sold a combined total of 564 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Tuesday?

Sep 8, 2015

I found: $141$ hamburgers and $423$ cheeseburgers.

#### Explanation:

Call $h$ and $c$ the number of the two items. You get:
$\left\{\begin{matrix}h + c = 564 \\ c = 3 h\end{matrix}\right.$

substitute the second into the first:
$h + 3 h = 564$
$4 h = 564$
$h = \frac{564}{4} = 141$ hamburgers
use this back into the second equation:

$c = 3 \cdot 141 = 423$ cheeseburgers.