Question

Erin bought 3 gallons of juice and 7 pounds of carrots for 4.80. Jinho bought 5 gallons of juice and 6 pounds of carrots for6.30. If the price of juice is the same for both Erin and Jinho, what is the price per gallon of juice?

1) $0.60
2) $0.70
3) $0.80
4) $0.90

Answer 1

After setting up and solving a system of linear equations, we find that the price per gallon of juice is $0.90.

Step-by-step explanation:

The question provided is a linear system in which we are asked to calculate the price per gallon of juice. We know that Erin bought 3 gallons of juice and 7 pounds of carrots for $4.80, and Jinho bought 5 gallons of juice and 6 pounds of carrots for $6.30. We can set up two equations with two variables (j for the price of juice per gallon and c for the price of carrots per pound) as follows:

3j + 7c = 4.80 (1)

5j + 6c = 6.30 (2)

Solving this system will give us the values of j and c. First, we could solve equation (1) for c:

c = (4.80 - 3j) / 7 (3)

Next, substitute (3) into equation (2):

5j + 6((4.80 - 3j) / 7) = 6.30

5j + (28.80 - 18j) / 7 = 6.30

35j + 28.80 - 18j = 44.10

17j = 15.30

j = 15.30 / 17

j = 0.90

Therefore, the price per gallon of juice is $0.90, which corresponds to option 4. We have used a step-by-step approach similar to how one might calculate the cost of groceries such as apples, bananas, grapes, and raspberries.