Question

A store Is having a sale on trall mix and jelly beans. For 3 pounds of trail mix and 2 pounds of jelly beans, the total cost is $10. For 5 pounds of trail mix and 6 pounds of jelly beans, the total cost Is $24. Find the cost for each pound of trail mix and each pound of jelly beans.

Answer 1

To solve for the cost per pound of trail mix and jelly beans, we can set up a system of equations based on the information given.

Let:
- \( x \) = cost per pound of trail mix
- \( y \) = cost per pound of jelly beans

From the problem, we have the following equations:

1. For 3 pounds of trail mix and 2 pounds of jelly beans costing $10:
\[
3x + 2y = 10 \tag{1}
\]

2. For 5 pounds of trail mix and 6 pounds of jelly beans costing $24:
\[
5x + 6y = 24 \tag{2}
\]

Now we can solve this system of equations. Let's use the method of substitution or elimination. Here, we will use the elimination method.

**Step 1: Multiply equation (1) by 3 to align coefficients with equation (2)**:

\[
3(3x + 2y) = 3 \times 10 \quad \Rightarrow \quad 9x + 6y = 30 \tag{3}
\]

**Step 2: Subtract equation (2) from equation (3)**:

\[
(9x + 6y) - (5x + 6y) = 30 - 24
\]
\[
4x = 6
\]
\[
x = \frac{6}{4} = \frac{3}{2} = 1.5
\]

**Step 3: Substitute \( x \) back into equation (1) to find \( y \)**:

\[
3(1.5) + 2y = 10
\]
\[
4.5 + 2y = 10
\]
\[
2y = 10 - 4.5
\]
\[
2y = 5
\]
\[
y = \frac{5}{2} = 2.5
\]

Now we have the final values:

- The cost per pound of trail mix \( x \) is **$1.50**.
- The cost per pound of jelly beans \( y \) is **$2.50**.

Thus, the cost per pound of trail mix is $1.50, and the cost per pound of jelly beans is $2.50.