A coffee distributor needs to mix a(n) Tanzanian coffee blend that normally sells for $10.50 per pound with a Rift Valley coffee blend that

Question

A coffee distributor needs to mix a(n) Tanzanian coffee blend that normally sells for $10.50 per pound with a Rift Valley coffee blend that normally sells for $12.00 per pound to create 70 pounds of a coffee that can sell for $10.99 per pound. How many pounds of each kind of coffee should they mix?

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Parker 2 weeks 2021-11-17T11:46:39+00:00 1 Answer 0 views 0

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    2021-11-17T11:47:41+00:00

    Answer:

    They should mix 13.72 pounds of Rift Valley coffee and 56.28 pounds of Tanzanian coffee.

    Step-by-step explanation:

    Given:

    A coffee distributor needs to mix a(n) Tanzanian coffee blend that normally sells for $10.50 per pound with a Rift Valley coffee blend that normally sells for $12.00 per pound to create 70 pounds of a coffee that can sell for $10.99 per pound.

    Now, to find the pounds of each kind of coffee they should mix.

    Let the pounds of Tanzanian coffee be x.

    Let the pounds of Rift Valley coffee be y.

    So, total pounds of coffee is:

    x+y=70

    x=70-y\ \ \ \ ........(1)

    Now, the total price of coffee per pound is:

    10.50(x)+12.00(y)=10.99(70)

    10.5x+12y=769.3

    Substituting the value of x from equation (1) we get:

    10.5(70-y)+12y=769.3

    735-10.5y+12y=769.3

    735+2.5y=769.3

    Subtracting both sides by 735 we get:

    2.5y=34.3

    Dividing both sides by 2.5 we get:

    y=13.72.

    Rift Valley coffee = 13.72 pounds.

    Now, substituting the value of y in equation (1):

    x=70-y\\x=70-13.72\\x=56.28.

    Tanzanian coffee = 56.28 pounds.

    Therefore, they should mix 13.72 pounds of Rift Valley coffee and 56.28 pounds of Tanzanian coffee.

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