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Math Help - Word problem.

  1. #1
    Ash
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    Word problem.

    How would I setup and answer this word problem?

    Two parts of pea gravel worth $10.00 per ton are mixed with one part of sand worth $8.00 per ton to form a base for road paving. If the bill for a project is $728.00, what is the approximate price per ton for the mixture?
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  2. #2
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    Quote Originally Posted by Ash View Post
    How would I setup and answer this word problem?

    Two parts of pea gravel worth $10.00 per ton are mixed with one part of sand worth $8.00 per ton to form a base for road paving. If the bill for a project is $728.00, what is the approximate price per ton for the mixture?
    I assume that the thing (whatever is it) is divided into two equal tons. One is work 10 and one is 8.

    Intotal we have, (if x is amount for half-amount).
    10x+8x=728
    18x=728
    x=40.44

    Then the full amount is 2x (because we considered half-amount).
    2x=80.88 tons

    The average amount being paid is:
    PRICE/QUANTITY.

    The price is 728 and the Quantity is 80.88

    Thus,
    728/80.88=9.000

    Thus it is 9 dollars.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Ash View Post
    How would I setup and answer this word problem?

    Two parts of pea gravel worth $10.00 per ton are mixed with one part of sand worth $8.00 per ton to form a base for road paving. If the bill for a project is $728.00, what is the approximate price per ton for the mixture?
    Let x tons be the total quantity, then there is 2x/3 tons of pea gravel, and x/3 tons
    of sand. So total cost is:

    10*(2x/3) + 8*(x/3) = 728 dollars.

    or:

    x*28 = 728*3,

    x = 728*3/28 = 78 tons.

    Therefor average price of mixture is total price divided by total quantity, which
    in this case is: 728/78 = 9.33 dollars per ton

    (actually 9 and 1/3 dollars per ton).

    RonL
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  4. #4
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    Hello, Ash!

    There are a number of approaches ... none are straight-forward.
    Here's another one . . .


    Two parts of pea gravel worth $10/ton are mixed with one part of sand worth $8/ton
    to form a base for road paving. .If the bill for a project is $728.00,
    what is the approximate price per ton for the mixture?

    Let x = number of tons of sand.
    . . At $8/ton, its cost is: 8x dollars.

    Let 2x = number of tons of pea gravel.
    . . At $10/ton, its cost is: 10(2x) = 20x dollars.

    The total cost Is $728: .8x + 20x .= .728 . . x = 26

    Hence, there is 26 tons of sand and 52 tons of pea gravel,
    . . a total of 78 tons of "stuff".

    The cost per ton is: .$728 78 .= .$28/3 . .$9.33

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