Find the cost of each pound of trail mix and each pound of jelly beans.

Question

A store is having a sale on trail mix and jelly beans. For 2

 pounds of trail mix and 12 pounds of jelly beans, the total cost is $37.

For 5 pounds of trail mix and 3 pounds of jelly beans, the total cost is $25. Find the cost for each pound of trail mix and each pound of jelly beans.

Answer 1

Hi Laura, set up a system of equations that represent the trail mix and jelly beans. let t represent the trail mix and j represent the jelly beans.

Equation 1, 2 pounds of trail mix and 12 pounds of jelly beans:

2t + 12j = 37

Equation 2, 5 pounds of trail mix and 3 pounds of jelly beans:

5t + 3p = 25

System of equations to solve:

2t + 12j = 37

5t + 3j = 25

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Multiply the second equation by -4 to eliminate the j terms:

2t + 12j = 37

-20t - 12j = -100

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-18t = -63

Divide both sides by -18:

t = 3.5

Substitute for t in the first equation:

2 * 3.5 + 12j = 37

7 + 12j = 37

Subtract 7 from both sides:

12j = 30

divide both sides by 12:

j = 2.5

Answer:

The trail mix costs $3.50 per pound and the jelly beans costs $2.50 per pound.

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