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Dean's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Deon $4.75 per pound, and type B coffee costs $5.90 per pound. This month, Deon made 144 pounds of the blend, for a total cost of $741.50. How many pounds of type B coffee did he use?

Respuesta :

TomShelby

Answer:

type B 50 pounds

type A 94 pounds

Explanation:

First we construct the equation system:

[tex]\left \{ {{A_q + B_q = 144} \atop {4.75A_q + 5.9B_q = 741.5}} \right. \\[/tex]

Now we clear one and replace:

[tex]A_q = 144 - B_q\\4.75A_q + 5.9B_q = 741.5\\4.75(144 - B_q) + 5.9B_q = 741.5[/tex]

And we can solve for type B:

[tex]4.75\times 144 - 4.75B_q + 5.9B_q = 741.5\\1.15B_q = 741.5 - 684\\B_q = 57.5 / 1.15 = 50[/tex]

And now we can solve for quantity of A as well:

A = 144 - 50 = 94

Finally we can check the answer if it is correct:

50 x 5.9 + 94 X 4.75 =

   295       +      446,5‬   = 741,5‬

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