Question

After cleaning house, Josh took a box of 29 used discs to sell at the flea market.

Some were computer games (which he sold for $2 each), some were music CDs (which he sold
for $3 each), and the rest were video DVDs (which he sold for $4 each). If Josh sold everything
(which included twice as many DVDs as computer games), and he made a total of $93, how
many of each type of disc did he sell?

Answer 1

Josh sold, 6 computer games, 12 video DVDs, and 11 music CDs

Explanation:

The given parameters are;

The number of used discs in the box Josh took to the flea market = 29

The price for which he sold the computer games = $2

The price for which he sold the music CDs = $3

The price for which he sold the video DVDs = $4

The number of DVDs = 2 × The number of computer games

The total amount Josh made = $93

Let C represent the number of computer games and let M represent the number of music CDs, and let V represent the number of DVDs, we have;

We have;

V = 2 × C...(1)

C + M + V = 29...(2)

2 × C + 3 × M + 4 × V = 93...(3)

By substituting the value of V, from equation (1), in equation (2), we have ;

C + M + (2 × C) = 29

∴ 3·C + M = 29

M = 29 - 3·C...(4)

By substituting the value of V, from equation (1) and the value of M, from equation (4) in equation (3), we have;

2 × C + 3 × M + 4 × V = 93...(3)

2·C + 3·M + 4·V = 93

2·C + 3·(29 - 3·C) + 4·(2·C) = 93

2·C + 87 - 9·C + 8·C = 93

C = 93 - 87 = 6

C = 6

The number of computer games = C = 6

V = 2 × C = 2 × 6 = 12

V = 12

The number of video DVDs = V = 12

M = 29 - 3·C = 29 - 3 × 6 = 11

M = 11

The number of music CDs = M = 11

Therefore, Josh sold, 6 computer games, 12 video DVDs, and 11 music CDs.