itsmichaelhere1
30.11.2020 •
Mathematics
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?
Solved
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Ответ:
Josh sold, 6 computer games, 12 video DVDs, and 11 music CDs
Step-by-step 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.
Ответ: