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Algebra

Sean and David had some allowance in the ratio of 3:7. They shared some money to buy a bracelet for their cousin. The ratio of the amount paid by Sean to the amount paid by David was 1:2. If David was left with $176 and Sean had spent 1/4 of his money, how much was the bracelet they bought?

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  1. Allowance:
    Sean gets 3x
    David gets 7x

    Shared amount for bracelet:
    Sean gave y
    David gave 2y

    Dave was left with 176 ----> 7x - 2y = 176 , #1
    Sean spent 1/4 of his money ----> 3x-y = (3/4)x
    12x - 4y = 3x
    9x - 4y = 0 , #2

    #1 times 2 ----> 14x - 4y = 352
    #2 leave it ----> 9x - 4y = 0
    subtract them
    5x = 352
    x = 70.40

    sub into #2:
    9(70.4) - 4y = 0
    y = 158.40

    cost of bracelet = y + 2y = 3y = $475.2

    check my arithmetic

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  2. let S = Sean’s allowance
    d = David’s allowance

    s/d = 3/7; s = 3d/7
    spent on bracelet:
    (Sean paid)/David paid = 1/2 = (1/4s)/(d - 176) = 0.25s/(d - 176)
    Substitute s = 3d/7:
    1/2 ≠ (0.25(3d/7))/(d - 176) = (3d (0.25))/(7(d - 176))
    2(3d)(0.25) = 7(d - 176)
    1.5d = 7d - 1232
    = -1232/-5.5 ; d = $224
    s = 3d/7 = (3(224))/7 = $96
    spent on bracelet : Sean = 1/4 (96) = $24
    David = 224 - 176 = $48
    cost of bracelet = amount paid by Sean + amount paid by David
    = $24 + $48 = $72
    The bracelet they bought cost $72.

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