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Math Help - Difficult Question

  1. #1
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    Difficult Question

    If peanuts cost $3 per kg and almonds cost $9 per kg, how many kilograms of almonds should be mixed with 4 kg of peanuts to get a mixture that costs $7.50 per kg?

    Please answer as soon as possible
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  2. #2
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    Re: Difficult Question

    Let x be the number of kg of peanuts and y be the number of kg of almonds. So 3x is the amount of money we're spending on peanuts and 9y is the amount of money we (or somebody) is spending on almonds. So the total spent is 3x + 9y and the amount of mixed nuts we're getting (or selling?) is x + y. So ...

    3x + 9y = (7.5)*(x+y)

    You could graph this as a line. Any number of possible combinations. But we're told to buy (or sell?) four kg of peanuts, so

    3*4 + 9y = (7.5)*(x+y)
    12 + 9y = (7.5)* (4 + y)

    Can you solve that for y?
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  3. #3
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    Re: Difficult Question

    Alternatively let m kg of Almonds be required to be mixed with 4 kg of peanuts to sell the mixture at 7.5 $ / kg
    Cost of Almonds = $ 9/kg Thus cost of m kg almond = $ 9m
    Cost of peanuts = $ 3 / kg Thus cost of 4 kg peanuts = $ 12.
    Cost of total mixture = $ 9m + $ 12
    Total quantity of mixture = ( m+ 4 ) kg
    It is to sold @ $ 7.5 / kg
    Thus we have
    9m + 12 = ( m+4) * 7.5
    just simplify for m and that would give the quantity of almonds required to be added to the mixture to be sold @ $ 7.5 per kg.
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