Question

At a grocery store, 5 candy bars and 6 power bars costs $15.25. At the same store, 5 candy bars and 12 power bars costs $24.25. Write a system of equations and use the elimination method to find the cost of one candy bar.

Answer 1

By setting up a system of equations and using the elimination method, we subtracted one equation from the other to eliminate one variable and found the cost of a power bar. We then substituted back to find that the cost of one candy bar is $1.25.

Step-by-step explanation:

To solve the problem of finding the cost of one candy bar using the elimination method, we first need to set up a system of equations based on the information provided.

Let the cost of a candy bar be c dollars and the cost of a power bar be p dollars. According to the problem:

• 5c + 6p = 15.25 (Equation 1)
• 5c + 12p = 24.25 (Equation 2)

To use the elimination method, we can subtract Equation 1 from Equation 2:

(5c + 12p) − (5c + 6p) = 24.25 − 15.25

This simplifies to:

6p = 9.00

Dividing both sides by 6, we find that:

p = 1.50

Now that we know the cost of a power bar, we substitute p = 1.50 into Equation 1:

5c + 6(1.50) = 15.25

5c + 9.00 = 15.25

Subtracting 9 from both sides, we get:

5c = 6.25

Finally, dividing both sides by 5:

c = 1.25

Therefore, the cost of one candy bar is $1.25.