Question

At a produce stand, 3 pounds of artichokes and 8 pounds of spinach cost a total of $51.00, while 9 pounds of artichoke and 4 pounds of spinach cost a total of $63.00. How much does a pound of spinach cost?

Answer 1

To find the cost of a pound of spinach, we can set up a system of equations and solve for the variable representing the cost of spinach. By solving this system, we find that a pound of spinach costs $1.80.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's assume that the cost of a pound of artichokes is A, and the cost of a pound of spinach is S.

1. From the first scenario, we can write the equation 3A + 8S = 51.00.
2. From the second scenario, we can write the equation 9A + 4S = 63.00.
3. We can solve this system of equations to find the value of S, the cost of a pound of spinach.
4. By multiplying the first equation by 3 and the second equation by -9, we can eliminate the variable A and solve for S. We get -9(3A + 8S) = -9(51), 27A - 72S = -459, and 27A + 12S = 567.
5. By adding the two equations, we eliminiate the variable A and solve for S. We get -72S + 12S = -459 + 567, -60S = 108, and S = 108/-60 = -1.80.

Therefore, a pound of spinach costs $1.80.