Karen's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Karen $5.50 per pound, and type B coffee costs $4.25 per pound. This month's blend used three times as many pounds of type B coffee as type A, for a total cost of $584.00. How many pounds of type A coffee were used?

32 lb

Step-by-step explanation:

Let a = number of pounds of type A coffee used.

Let b = number of pounds of type B coffee used.

From the statement:

"This month's blend used three times as many pounds of type B coffee as type A"

we get this equation:

b = 3a

"Type A coffee costs Karen $5.50 per pound, and type B coffee costs $4.25 per pound."

She spend (in dollars) 5.50a + 4.25b, but since b = 3a, we get

5.5a + 4.25 (3a) = 5.5a + 12.75a.

She spent $584, so

5.5a + 12.75a = 584

18.25a = 584

a = 32

She used 32 lb of type A coffee.