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Math Help - Delivery

  1. #1
    Junior Member
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    Delivery

    A delivery agent delivers goods to four stores and then returns to the warehouse. The driver delivers 1/4 of the load to the 1st store, then 1/2 of the remainder at the next store, then 1/4 of the remainder at the 3rd store and 1/3 of what is left to the 4th store. The agent has 480 units of goods to go back to the warehouse. How many units of goods did he deliver?
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  2. #2
    MHF Contributor
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    Let x = total number of goods initially with the driver before distributions.

    "The driver delivers 1/4 of the load to the 1st store,..."
    Ist store receives (1/4)x = x/4
    Remaining load = x -x/4 = (3/4)x = 3x/4

    "... then 1/2 of the remainder at the next store,..."
    2nd store receives (1/2)(3x/4) = 3x/8
    Remaining load = 3x/4 -3x/8 = (2*3x -3x)/8 = 3x/8

    "... then 1/4 of the remainder at the 3rd store..."
    3rd store receives (1/4)(3x/8) = 3x/32
    Remaining load = 3x/8 -3x/32 = (4*3x -3x)/32 = 9x/32

    "... and 1/3 of what is left to the 4th store."
    4th store receives (1/3)(9x/32) = 3x/32
    Remaining load = 9x/32 -3x/32 = 6x/32

    "The agent has 480 units of goods to go back to the warehouse."
    That means 6x/32 = 480, so,
    6x = 480*32
    x = (480*32)/6
    x = 80*32
    x = 2560

    "How many units of goods did he deliver?"
    He has 2560 initially, then he has 480 returned, so,
    2560 -480 = 2080 delivered. -----answer.

    Check:
    1st store, x/4 = 2560/4 = 640 received
    2nd store, 3x/8 = 3*2560/8 = 960
    3rd store, 3x/32 = 3*2560/32 = 240
    4th store, 3x/32 also = 240 also
    ---------
    Total = 640+960+240+240 = 2080 ----it checks, so, OK.
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  3. #3
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    Thanks very much ticbol!
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