Algebra Word Problem

Question

Tammy's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Tammy $4.10 per pound, and type B coffee costs $5.65 per pound. This month's blend used twice as many pounds of type B coffee as type A, for a total cost of $539.00. How many pounds of type A coffee were used?

Answer 1

Let "A" represent the amount (number of pounds) of Type A coffee and let "B" represent the amount (number of pounds) of Type B coffee.

Then "This month's blend used twice as many pounds of type B coffee as type A" means:

2A = B

And "Type A coffee costs . . . $4.10 per pound, and type B coffee costs $5.65 per pound . . . for a total cost of $539.00" means:

4.10A + 5.65B = 539.00

Since "2A" is the same as "B" (from the 1st equation) then we can substitute "2A" in place of "B" making the 2nd equation:

4.10A + 5.65(2A) = 539.00

4.10A + 11.30A = 539.00

15.40A = 539.00

A = 539.00/15.40

A = 35

So there were 35 pounds of Type A coffee used