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?

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.