# Phillip bought 12 used CDs and DVDs. CDs cost $2 each, and DvDs cost$3 each. He spent $31, not including tax. How many DVDs did Phillip buy? ##### 1 Answer Jan 7, 2017 Phillip bought 7 DVDs #### Explanation: First, let's define the number of CDs Phillip bought as $\textcolor{red}{C}$and the number of DVDs Phillip bought as $\textcolor{b l u e}{D}$. We can now write a couple of equations. First, the number number of items Phillip purchased can be written as: $\textcolor{red}{C} + \textcolor{b l u e}{D} = 12$The cost of the items Phillip purchased can be written as: $2color(red)(C) + $3color(blue)(D) =$31

We can now solve the first equation for $\textcolor{red}{C}$ or the number of CDs Phillip bought:

$\textcolor{red}{C} + \textcolor{b l u e}{D} - \textcolor{b l u e}{D} = 12 - \textcolor{b l u e}{D}$

$\textcolor{red}{C} + 0 = 12 - \textcolor{b l u e}{D}$

$\textcolor{red}{C} = 12 - \textcolor{b l u e}{D}$

Because we know what $\textcolor{red}{C}$ equals we can substitute $12 - \textcolor{b l u e}{D}$ for $\textcolor{red}{C}$ in the second equation and solve for $\textcolor{b l u e}{D}$ or the number of DVDs Phillip bought:

($2 xx (color(red)(12 - color(blue)(D)))) +$3color(blue)(D) = $31 $24 - $2color(blue)(D) +$3color(blue)(D) = $31 $24 + (-$2 +$3)color(blue)(D) = $31 $24 + $1color(blue)(D) =$31

$24 +$1color(blue)(D) = $31 $24 - color(green)($24) +$1color(blue)(D) = $31 - color(green)($24)

0 + $1color(blue)(D) =$7

$1color(blue)(D) =$7

($1color(blue)(D))/($1) = ($7)/($1)

(cancel($1)color(blue)(D))/cancel(($1)) = (cancel($)7)/cancel(($1))

$\textcolor{b l u e}{D} = 7$