Question

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?

Answer 1

Phillip bought 7 DVDs

Explanation:

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)`.

We can now write a couple of equations.

First, the number number of items Phillip purchased can be written as:

`color(red)(C) + color(blue)(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 `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`