Question

Rob spent $85 on 5 daylilies and 6 geraniums. Jenny spent $125 on 5 daylilies and 10 geraniums.

What is the cost of one daylily and the cost of one geranium?

Answer 1

By setting up a system of linear equations based on the purchases and using the elimination method, we find that the cost of one daylily is $5 and the cost of one geranium is $10.

Step-by-step explanation:

The question involves a system of linear equations, which is a mathematical way to solve for the cost of individual items based on total purchases. To find the cost of one daylily and one geranium, we have to set up two equations based on the information given:

Let D represent the cost of one daylily and G represent the cost of one geranium. We have the following equations based on Rob and Jenny's spending:

1. 5D + 6G = $85 (Rob's purchase)
2. 5D + 10G = $125 (Jenny's purchase)

By using either substitution or elimination method, we can solve this system of equations. If we subtract the first equation from the second, we cancel out the daylilies:

5D + 10G - (5D + 6G) = $125 - $85

This simplifies to 4G = $40, giving us G = $10. Now, we can plug this back into the first equation to solve for D:

5D + 6(10) = $85

5D + $60 = $85

5D = $85 - $60

5D = $25

Therefore, D = $5. The cost of one daylily is $5, and the cost of one geranium is $10.