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13 May, 22:50

Aunt Maura spends $12 on mangos at a local merchant. If Aunt Maura bought the mangos at a shopping center instead, she could purchase an extra pound of mangos for the same amount of money. The mangos are $1 cheaper per pound at the shopping center than at the local merchant. What is the price per pound of mangos at the local merchant?

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  1. 14 May, 00:45
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    Price per pound of mangos at the local merchant = 4

    Explanation:

    We are going to propose a system of 2 equations with 2 unknowns

    a) P * Q = 12

    b) (P - 1) * (Q + 1) = 12

    Where

    P is Price and Q is Quantity

    and

    Equation a) represents local merchant and Equation b) represents the shopping center.

    Now we use the substitution method to solve this:

    First we clear quantity from equation a)

    a) P * Q = 12

    Q = 12 / P

    Then we replace it in equation b)

    b) (P - 1) * (Q + 1) = 12

    (P - 1) * ((12 / P) + 1) = 12

    And now we solve the resulting equation

    (P - 1) * ((12 / P) + 1) = 12

    (12P / P) + P - (12 / P) - 1 = 12

    12 + P - (12 / P) - 1 = 12

    P - (12 / P) = 12 - 12 + 1

    P - (12 / P) = 1

    (12 / P) = - 1 + P

    12 = P (-1 + P)

    12 = - P + P ^ 2

    0 = - P + P ^ 2 - 12

    Calculating the routs

    x1 = - 3

    x2 = 4

    We choose the positive one, with means the price is 4.

    So the price is 4 and the quantity 3 in the local merchant. In the shopping center the price is 3 and the quantity 4. Both gives the total amount of 12 dollars.
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