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