Answer: Let's use the variables "r" and "c" to represent the cost of one rose and one carnation, respectively.
From the first sentence, we know that 8 roses and 5 carnations cost $31.75. So we can write the equation:
8r + 5c = 31.75
From the second sentence, we know that 1 rose and 3 carnations cost $5.75. So we can write the equation:
r + 3c = 5.75
Now we have two equations with two variables. We can use substitution or elimination to solve for "c". Let's use substitution:
r = 5.75 - 3c (from the second equation)
Substitute this expression for "r" into the first equation:
8(5.75 - 3c) + 5c = 31.75
Simplify and solve for "c":
46 - 24c + 5c = 31.75
-19c = -14.25
c = 0.75
Therefore, the cost for a carnation is $0.75.
Explanation: