Math

A confectioner perchased several boxes of candy for $6. He gave five boxes to his children, and sold the rest at 10 cents more per box than he had paid for them, and made a profit of 25% on his original cost. How much did a box of candy cost him?

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asked by Lina
  1. 1.25 * 6 = 7.5
    profit = 1.5

    let cost per box = c
    sales price = s = c+.1
    bought n
    gave away 5
    sold (n-5)

    cost = n c = 6 so n=6/c
    sales = (n-5)(c+.1)
    so
    (n-5)(c+.1) - 6 = 1.5

    (6/c -5)(c+.1) = 7.5

    6 -5c + .6/c -.5 = 7.5

    -5c + .6/c = 2
    -5 c^2 -2 c + .6 = 0

    5 c^2 + 2 c -.6 = 0

    c = [ -2 +/- sqrt(4 + 12) ]/10

    c = [-2 + 4 ]/10

    c = 0.2 or 20 cents

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    posted by Damon
  2. How would you check it?

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    posted by Lina
  3. If c = .2
    n = 6/.2 = 30
    so sold 25 for .3 so got 25*.3 = 7.5 sure enough

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    posted by Damon
  4. thank you!

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    posted by Lina
  5. You are welcome :)

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    posted by Damon
  6. Bought X boxes.
    Sold (x-5) boxes.

    Cost = $Y per box
    Selling price = $(y+0.1) per box.

    P = $6 * 1.25 = 7.50 = Sale price.

    (x-5)(y+0.1) = 7.50
    xy + 0.1x - 5y - 0.5 = 7.5

    Eq1: xy + 0.1x - 5y = 8

    Eq2: xy = $6.00
    Y = 6/x
    In Eq1, replace Y with 6/x:
    6 + 0.1x - 30/x = 8
    0.1x - 30/x = 2
    Multiply both sides by X:
    0.1x^2 - 30 = 2x
    0.1x^2 - 2x - 30 = 0
    Multiply both sides by 10:
    x^2 - 20x - 300 = 0
    (x+10)(x-30) = 0

    x+10 = 0, X = -10.
    x-30 = 0, X = 30 Boxes bought.

    x-5 = 30 - 5 = 25 Boxes sold.

    30 * y = $6.00
    Y = $0.20 per box. = Cost.

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    posted by Henry

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