Rachel's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Rachel $4.20 per pound, and type B coffee costs $5.50 per pound. This month's blend used four times as many pounds of type B coffee as type A, for a total cost of $864.60. How many pounds of type A coffee were used?

Hey there! I'm happy to help!

Let's call the use the variables A and B to represent the number of pounds used for those types of coffee and set up a system of equations below to solve.

4.20A+5.50B=864.60

B=4A

Let's replace B in the first equation with 4A.

4.20A+5.50(4A)=864.60

Undo the parentheses.

4.20A+22A=864.60

Combine like terms.

26.2A=864.6

Divide both sides by 26.2

A=33

Therefore 33 pounds of type A coffee were used in this month's blend at Rachel's Coffee Shop.

Have a wonderful day! :D

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