I need help!

Michael. · Jan 19, 2012, 10:20 PM

Toms coffee shop makes a blend that Is a mixture of two types of coffee. Type A coffe cost $5.80 per pound, and type B coffe costs $4.55 per pound. This months blend used three times as many pounds of type B coffee then type A, for a total cost of $602.95. How many pounds of type A coffee were used?

corrigan · Jan 19, 2012, 11:09 PM

Let $A$ be the number of pounds of type A coffee used, and let $B$ be the number of pounds of type B coffee used. Since this months blend used three times as many pounds of type B coffee then type A coffee, then we have

$3A=B$

And since the total cost of this month's blend is $602.95, and type A is $5.80 and type B is $4.55, then we have

$602.95 = 5.80 \cdot A + 4.55 \cdot B$ .

Since $3A=B$ , then we can substitute for $B$ and get

$602.95 = 5.80 \cdot A + 4.55 \cdot (3A)$ .

Now we solve for $A$ .

$602.95 = 5.80 \cdot A + 13.65 \cdot A$

$\Rightarrow 602.95 = 19.45 \cdot A$

$\Rightarrow A= \frac{602.95}{19.45}= 31$

So 31 pounds of type A.

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