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?

Option 1: $3.50
Option 2: $4.50
Option 3: $5.00
Option 4: $6.00

Answer 1

By setting up equations from the given scenarios and using the method of elimination, we determine that the cost per pound of spinach is $4.50. This is achieved by equating the combined cost of artichokes and spinach from both scenarios and solving for the unknown price per pound of spinach.

Step-by-step explanation:

To determine the cost of a pound of spinach from the given scenarios at the produce stand, we can set up two equations to represent each scenario and solve for the unknowns, which are the cost per pound of artichokes and spinach. We'll denote the cost per pound of artichokes as 'a' and the cost per pound of spinach as 's'.

For the first scenario, the equation based on the total cost is:

3a + 8s = $51.00

For the second scenario, we have:

9a + 4s = $63.00

To find the value of 's', we can multiply the first equation by 3, giving us 9a + 24s = $153.00, and subtract the second scenario's equation from this result:

• 9a + 24s = $153.00
• -(9a + 4s = $63.00)

This gives us: 20s = $90.00, and by dividing both sides by 20, we get s = $4.50. Therefore, the cost per pound of spinach is $4.50, which corresponds to Option 2.