Question

Charmaine's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Charmaine $5.55 per pound, and type B coffee costs $4.10 per pound. This month's blend used three times as many pounds of type B coffee as type A, for a total cost of $446.25. How many pounds of type A coffee were used?

Number of pounds of type A coffee:

Answer 1

Charmaine's Coffee Shop used approximately 25 pounds of type A coffee in their blend, calculated by setting up and solving an equation based on the given prices and total cost.

Step-by-step explanation:

To solve for the number of pounds of type A coffee used by Charmaine's Coffee Shop, we can set up a system of equations based on the given prices per pound and the total cost. Let's denote the weight of type A coffee as 'x' pounds and that of type B as '3x' pounds, since it's given that type B coffee is used three times as much as type A.

The cost per pound for type A is $5.55, and for type B is $4.10. The total cost for the blend is $446.25. Using this information, we can create the following equation:

5.55x + 4.10(3x) = 446.25

Simplifying this equation, we get:

5.55x + 12.30x = 446.25

Adding the x terms together gives us:

17.85x = 446.25

Dividing both sides by 17.85 to solve for x, we get:

x = 446.25 / 17.85

x ≈ 25

Therefore, approximately 25 pounds of type A coffee were used.