Question

The florist charges $31.75 for eight roses and five carnations. For one rose and three carnations, it costs $5.75. What is the cost for a carnation?

Answer 1

To determine the cost of a single carnation, we derived equations from the provided cost scenarios and solved them, which revealed that the cost of one carnation is $0.75.

Step-by-step explanation:

The student is asking to find the cost of a single carnation given the total cost of combinations of roses and carnations. We have two purchase scenarios to create equations and solve for the price of a single carnation:

1. 8 roses and 5 carnations cost $31.75.
2. 1 rose and 3 carnations cost $5.75.

Let's designate R as the cost of a rose and C as the cost of a carnation. Therefore, we have two equations:

• 8R + 5C = 31.75
• 1R + 3C = 5.75

To solve these equations, we can use substitution or elimination. Let us simplify the problem by multiplying the second equation by 8, so both equations have the same number of roses.

• 8R + 5C = 31.75
• 8R + 24C = 46.00

Subtracting the first equation from the second equation yields:

• 19C = 46.00 - 31.75
• 19C = 14.25

Dividing 14.25 by 19, we find

• C = 0.75

Thus, the cost of a single carnation is $0.75.