Question

Chau's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Chau $5.85 per pound, and type B coffee costs $4.50 per pound. This month's blend used twice as many pounds of type B coffee as type A, for a total cost of $475.20. How many pounds of type A coffee were used?

A) 40 pounds of type A coffee
B) 80 pounds of type A coffee
C) 30 pounds of type A coffee
D) 60 pounds of type A coffee

Answer 1

By setting up a system of equations and using the given information, we calculate that 32 pounds of type A coffee were used in Chau's Coffee Shop blend. However, the calculated figure does not match any of the provided options, suggesting an error in the question or answer choices.

Step-by-step explanation:

To determine how many pounds of type A coffee were used, we can set up a system of equations based on the problem's statement.

Let's denote the number of pounds of type A coffee as A and the number of pounds of type B coffee as B. According to the problem, twice as many pounds of type B coffee were used compared to type A, so we can represent this as B = 2A.

Next, we know that the total cost for the coffee is $475.20. This can be represented by the equation 5.85A + 4.50B = 475.20.

Since B is twice A, we can substitute 2A for B in the cost equation, giving us 5.85A + 4.50(2A) = 475.20. Adding together the terms with A gives us 5.85A + 9A = 475.20 or 14.85A = 475.20.

To find the value of A, we divide both sides by 14.85: A = 475.20 / 14.85 = 32.

So, 32 pounds of type A coffee were used, which is not one of the options provided (A) 40 pounds, (B) 80 pounds, (C) 30 pounds, (D) 60 pounds, indicating a possible error in the choices given or in the problem setup.