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7 February, 03:40

Ace Electronics, Hi-Fi Stereo, and CD World buy a total of 195 DVD players from the same distributor each month. Because CD World buys 35 more units than the other two stores combined, CD World's cost is only $160 per unit. The players cost Hi-Fi $165 each and Ace $170 each. How many players does each retailer buy each month if the distributor receives $31,750 each month from the sale of the players to the three stores?

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  1. 7 February, 07:30
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    Ace Electronics buys 30, Hi-Fi Stereo buys 50, and CD World buys 115

    Step-by-step explanation:

    Let x represent the number of items Ace Electronics buys

    Let y represent the number of items Hi-Fi Stereo buys

    Let z represent the number of items CD World buys

    Since Ace Electronics, Hi-Fi Stereo, and CD World buy a total of 195 DVD players:

    x + y + z = 195 (1)

    Since CD World buys 35 more units than the other two stores combined:

    z = x + y + 35 (2)

    If you substitute z in equation 1 from equation 2:

    x + y + (x + y + 35) = 195

    2 (x + y) = 195 - 35

    x + y = 80 (3)

    Since z = x + y + 35:

    z = 80 + 35

    z = 115

    Since CD World's cost is $160 per unit, Hi-Fi 's cost is $165 per unit and Ace Electronics's cost is $170 per unit and the total payment received is $31,750

    170x + 165y + 160z = 31750 (Substitute x from equation 3 and z as 115)

    170 (80-y) + 165y + 160 (115) = 31750

    13600 - 170y + 165y + 18400 = 31750

    32000 - 5y = 31750

    5y = 250

    y = 50

    Since x + y = 80:

    x + 50 = 80

    x = 30
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