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23 February, 02:40

Austin's Coffee Shop makes a blendd that is a mixture of two types of coffee. Type a coffee costs bill $5.70 per pound and type b coffee costs $4.65 per pound. This month bill made 181 pounds of the blend, for a total cost of $943.50. How many pounds of type A coffee did he use?

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  1. 23 February, 05:50
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    He use 97 pound of type A coffee

    Step-by-step explanation:

    Let's call A the pounds of type A coffee that Austin used this month and B the pounds of type B coffee that Austin used this month.

    From the sentence: Type A coffee costs bill $5.70 per pound and type B coffee costs $4.65 per pound and the total cost is $943.50, we can formulated the equation 1 as:

    5.70*A + 4.65*B=943.50

    Because the total cost is the sum of the cost of every type of coffee.

    Additionally, from the sentence: This month bill made 181 pounds of the blend, we can formulate the equation 2 as:

    A + B = 181

    Solving for B, we get:

    B = 181 - A

    Now, for find the value of A we need to replacing this last equation on equation 1, and solving for A as:

    5.70*A + 4.65*B=943.50

    5.70*A + 4.65 * (181-A) = 943.50

    5.70*A + 841.65 - 4.65*A = 943.50

    5.70*A - 4.65*A = 943.50 - 841.65

    1.05*A = 101.85

    A = 101.85/1.05

    A = 97

    So, this month, he use 97 pound of type A coffee.
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