High School

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Lisa's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Lisa $5.80 per pound, and type B coffee costs $4.45 per pound. This month, Lisa made 145 pounds of the blend, for a total cost of $765.40. How many pounds of type A coffee did she use?

Answer :

Final answer:

To find out how many pounds of type A coffee Lisa used, we set up a system of equations based on weight and cost, and by solving, we determined that Lisa used 89 pounds of type A coffee.

Explanation:

The student's question is related to creating a blend of two types of coffee and determining the quantity of each type needed for the blend given the costs and total weight. Let's denote the pounds of type A coffee as A and the pounds of type B coffee as B. From the information given, we know the following:

  • The cost of type A coffee per pound is $5.80.
  • The cost of type B coffee per pound is $4.45.
  • The total weight of the blend is 145 pounds.
  • The total cost of the blend is $765.40.

We can set up a system of two equations to find the values of A and B.

Weight equation: A + B = 145 pounds

Cost equation: 5.80A + 4.45B = $765.40

Now, we can solve for A using substitution or elimination. For example, using substitution, we can express B as (145 - A) from the weight equation and substitute it into the cost equation:

5.80A + 4.45(145 - A) = $765.40

Simplifying this, we have:

5.80A + 645.25 - 4.45A = $765.40

1.35A = $765.40 - 645.25

1.35A = $120.15

A = $120.15 / 1.35

A = 89 pounds

So, Lisa used 89 pounds of type A coffee in the blend.

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