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?

Question

Eli Assouline · Accepted Answer

Phillip bought 7 DVDs

First, let's define the number of CDs Phillip bought as #color(red)(C)# and the number of DVDs Phillip bought as #color(blue)(D)#. Now, we are able to write a few equations. First, the quantity of goods Phillip bought can be expressed as follows: #color(red)(C) + color(blue)(D) = 12# The price that Phillip paid for the goods is as follows: #$2color(red)(C) + $3color(blue)(D) = $31# We can now solve the first equation for #color(red)(C)# or the number of CDs Phillip bought: #color(red)(C) + color(blue)(D) - color(blue)(D) = 12 - color(blue)(D)# #color(red)(C) + 0 = 12 - color(blue)(D)# #color(red)(C) = 12 - color(blue)(D)# Because we know what #color(red)(C)# equals we can substitute #12 - color(blue)(D)# for #color(red)(C)# in the second equation and solve for #color(blue)(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))# #color(blue)(D) = 7#

Kennedy Adams · Answer

undefined Phillip bought 6 DVDs.