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Math Help - 8 bags from the first shop

  1. #1
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    8 bags from the first shop

    I need help in the below problem
    Thanks

    Jack bought 8 bags from the first shop then, he bought three more identical bags at $42.50 each from the second shop. The average cost of all his bags was decreased by $1.50.what was the total cost of 11 bags.
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  2. #2
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    Re: 8 bags from the first shop

    Let x be the price of each of the 8 bags from the first shop. Find the following (use x if necessary).

    (1) Price of 8 bags from the first shop
    (2) Average price of bag from the first shop
    (3) Total price of bags from the second shop
    (4) Total price of bags from both shops
    (5) Total price of bags from both shops
    (6) Average price of bags from both shops


    Then the equation is: the answer for (2) - the answer for (6) = 1.50
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    Re: 8 bags from the first shop

    Thanks but it is stated that "The average cost of all his bags was decreased by $1.50' which I assumed that all the 11 bags were decreased by 1.50 .; this I find is not possible. Here is where I get stuck.
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    Re: 8 bags from the first shop

    Quote Originally Posted by kingman View Post
    it is stated that "The average cost of all his bags was decreased by $1.50' which I assumed that all the 11 bags were decreased by 1.50 .; this I find is not possible.
    I agree. When all 11 bags were purchased, i.e., when the cost of each bag was fixed, the average was also fixed. Therefore, I understand the phrase "The average cost of all his bags was decreased by $1.50" to mean that the average cost of all 11 bags was $1.50 less than the average cost of the first 8 bags (which were "all his bags" after the first purchase).
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    Re: 8 bags from the first shop

    Quote Originally Posted by kingman View Post
    Jack bought 8 bags from the first shop then, he bought three more identical bags at $42.50 each from the second shop. The average cost of all his bags was decreased by $1.50.what was the total cost of 11 bags.
    Should be worded more clearly, like:
    Jack bought 8 bags from the first shop.
    Then, he bought three more identical bags at $42.50 each from the second shop:
    this purchase reduced the average cost of all his bags by $1.50.
    What was the total cost of the 11 bags?

    x - (8x + 127.50)/11 = 1.50
    Solve for x, which will be average cost of first 8 bags.
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  6. #6
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    Re: 8 bags from the first shop

    Thanks.
    soving the equation gives x=48 and then would give the original price for each of the 8 bags from first shop = 48+1.50=$49.50.
    In addition the price of each of the 3 bags from the second shop would be reduced to $46.50 which is not possible.
    Simple reasoning say that averaging the 11 bags would give a value more than the price from each of 3 bags from second shop.
    This is confusing!
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    Re: 8 bags from the first shop

    Quote Originally Posted by kingman View Post
    soving the equation gives x=48
    Yes.

    Quote Originally Posted by kingman View Post
    and then would give the original price for each of the 8 bags from first shop = 48+1.50=$49.50.
    No. By assumption, x is the original price for each of the 8 bags from first shop.
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  8. #8
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    Re: 8 bags from the first shop

    Thanks for the reply .
    Incidentally I have a solution which is entirely different from yours and I wonder whether the below reasoning is correct.
    Any comment is most welcome. I suspect some of the assumptions and reasoning is wrong but the final answer is correct.
    Thanks

    The average cost of 11 bags was decreased by $1.50,
    the total cost of 11 bags was decreased by: $1.50 x 11 = $16.50.

    The decrease of $16.50 was due to procurement of 3 bags from the second shop,
    so each bag purchased from the second shop was decreased by: $16.50/3 = $5.50.

    The cost of one bag from the first shop was: $42.50 + $5.50 = $48.00

    The total cost of 11 bags was:
    $48.00 x 8 + $42.50 x 3
    = $384.00 + $127.50
    = $511.50
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    Re: 8 bags from the first shop

    Quote Originally Posted by emakarov View Post
    Let x be the price of each of the 8 bags from the first shop. Find the following (use x if necessary).

    (1) Price of 8 bags from the first shop
    (2) Average price of bag from the first shop
    ?? You said "let x be the price of each of the 8 bags from the first shop so you were assuming each bag cost the same thing. Under that assumption, the "Average price of bag from the first shop" is x. It would be more general to say "Let x be the average price of each of the 8 bags from the first shop but you would still have x as the answer to (2).

    (3) Total price of bags from the second shop
    (4) Total price of bags from both shops
    (5) Total price of bags from both shops
    (6) Average price of bags from both shops


    Then the equation is: the answer for (2) - the answer for (6) = 1.50
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