Question

Scott's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Scott $4.10 per pound, and type B coffee costs $5.25 per pound. This month, Scott made 150 pounds of the blend, for a total cost of $712.75 . How many pounds of type B coffee did he use?

Answer 1

To determine the pounds of type B coffee used in the blend, set up two linear equations based on the total weight and cost of the coffee blend. Solve one equation for a variable and substitute it into the other equation, leading to the solution.

Step-by-step explanation:

To solve the problem of how many pounds of type B coffee Scott used in his blend, we will use a system of linear equations. Let's denote the amount of type A coffee as x pounds and the amount of type B coffee as y pounds. The two equations that represent the situation are:

• x + y = 150 (because the total amount of the blend is 150 pounds)
• 4.10x + 5.25y = 712.75 (because this represents the total cost of the blend)

We can solve for x in the first equation, getting x = 150 - y, and substitute this into the second equation:
4.10(150 - y) + 5.25y = 712.75

Multiplying out the terms and combining like terms gives us the amount of type B coffee used in the blend.