Question

A store Is having a sale on trail mix and jelly beans. For 8 pounds of trail mix and 3 pounds of jelly beans, the total cost is $29. For 2 pounds of trall mix and 5 pounds of jelly beans, the total cost is $20. Find the cost for each pound of trail mix and each pound of jelly beans.

Answer 1

Let \( x \) be the cost per pound of trail mix and \( y \) be the cost per pound of jelly beans. We can set up the following system of equations based on the information provided:

1. For 8 pounds of trail mix and 3 pounds of jelly beans costing $29:
\[
8x + 3y = 29
\]

2. For 2 pounds of trail mix and 5 pounds of jelly beans costing $20:
\[
2x + 5y = 20
\]

Now we will solve this system of equations.

### Step 1: Solve the second equation for \( x \)

From the second equation:
\[
2x + 5y = 20
\]

We can express \( x \) in terms of \( y \):
\[
2x = 20 - 5y
\]
\[
x = 10 - \frac{5}{2}y
\]

### Step 2: Substitute \( x \) into the first equation

Now, we plug this expression for \( x \) into the first equation:
\[
8(10 - \frac{5}{2}y) + 3y = 29
\]

### Step 3: Distribute and simplify

Distributing \( 8 \):
\[
80 - 20y + 3y = 29
\]

Combining like terms:
\[
80 - 17y = 29
\]

### Step 4: Solve for \( y \)

Subtract \( 80 \) from both sides:
\[
-17y = 29 - 80
\]
\[
-17y = -51
\]

Now divide by \( -17 \):
\[
y = 3
\]

### Step 5: Substitute \( y \) back to find \( x \)

Now, substitute \( y = 3 \) back into the expression for \( x \):
\[
x = 10 - \frac{5}{2}(3)
\]
\[
x = 10 - \frac{15}{2}
\]
\[
x = 10 - 7.5
\]
\[
x = 2.5
\]

### Conclusion

The costs are:
- The cost per pound of trail mix \( x \) is **$2.50**.
- The cost per pound of jelly beans \( y \) is **$3.00**.