# Ralph bought some magazines at $4 each and some dvds at$12 each. He spent $144 and bought a total of 20 items. How many magazines and how many movies did he buy? ##### 1 Answer Mar 20, 2018 #### Answer: Ralph bought $12$magazines and $8$dvds. #### Explanation: Let $m$be the number of magazines Ralph bought and $d$be the number of dvds he bought. "Ralph bough some magazines at $4 each and some dvds at $12 each. He spent $144."

$\left(1\right) \implies 4 m + 12 d = 144$

"He bought a total of $20$ items."

$\left(2\right) \implies m + d = 20$

We now have two equations and two unknowns, so we can solve the linear system.

From $\left(2\right)$ we find:

$\left(3\right) \implies m = 20 - d$

Substituting $\left(3\right)$ into $\left(1\right)$:

$4 \left(20 - d\right) + 12 d = 144$

$80 - 4 d + 12 d = 144$

$8 d + 80 = 144$

$8 d = 64$

$\implies \textcolor{b l u e}{d = 8}$

We can use this result in $\left(3\right)$:

$m = 20 - \left(8\right)$

$\implies \textcolor{b l u e}{m = 12}$

Hence, Ralph bought $12$ magazines and $8$ dvds.