Questions: Equations and Inequalities Solving a value mixture problem using a linear equation Lisa's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Lisa 4.50 per pound, and type B coffee costs 5.65 per pound. This month, Lisa made 122 pounds of the blend, for a total cost of 631.80. How many pounds of type B coffee did she use? Number of pounds of type B coffee:

Equations and Inequalities Solving a value mixture problem using a linear equation Lisa's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Lisa 4.50 per pound, and type B coffee costs 5.65 per pound. This month, Lisa made 122 pounds of the blend, for a total cost of 631.80. How many pounds of type B coffee did she use? Number of pounds of type B coffee:
Transcript text: Equations and Inequalities Solving a value mixture problem using a linear equation Lisa's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Lisa $\$ 4.50$ per pound, and type B coffee costs $\$ 5.65$ per pound. This month, Lisa made 122 pounds of the blend, for a total cost of $\$ 631.80$. How many pounds of type B coffee did she use? Number of pounds of type B coffee: $\square$
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Solution

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Solution Steps

To solve this problem, we need to set up a system of linear equations based on the given information. Let \( x \) be the number of pounds of type A coffee and \( y \) be the number of pounds of type B coffee. We have two equations:

  1. \( x + y = 122 \) (total pounds of coffee)
  2. \( 4.50x + 5.65y = 631.80 \) (total cost of the blend)

We can solve this system of equations to find the value of \( y \).

Step 1: Define Variables and Equations

Let \( x \) be the number of pounds of type A coffee and \( y \) be the number of pounds of type B coffee. We are given the following information:

  • The total weight of the coffee blend is 122 pounds.
  • The total cost of the coffee blend is \$631.80.
  • Type A coffee costs \$4.50 per pound.
  • Type B coffee costs \$5.65 per pound.

We can set up the following system of linear equations: \[ \begin{cases} x + y = 122 \\ 4.50x + 5.65y = 631.80 \end{cases} \]

Step 2: Solve the System of Equations

We solve the system of equations to find the values of \( x \) and \( y \).

From the solution, we have: \[ x = 50.0000 \] \[ y = 72.0000 \]

Final Answer

\(\boxed{y = 72}\)

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