Question

1. perry and julia each improved their yards by planting rose bushes and geraniums. they bought their supplies from the same store. perry spent $80 on 8 rose bushes and 4 geraniums. julia spent $95 on 11 rose bushes and 4 geraniums. what is the cost of one rose bush and the cost of one geranium?

Explanation:

Step1: Define variables

Let \( r \) be the cost of one rose bush and \( g \) be the cost of one geranium.

Step2: Set up equations

From Perry's purchase: \( 8r + 4g = 80 \)
From Julia's purchase: \( 11r + 4g = 95 \)

Step3: Subtract the first equation from the second

\( (11r + 4g) - (8r + 4g) = 95 - 80 \)
\( 11r + 4g - 8r - 4g = 15 \)
\( 3r = 15 \)

Step4: Solve for \( r \)

\( r = \frac{15}{3} = 5 \)

Step5: Substitute \( r = 5 \) into the first equation to find \( g \)

\( 8(5) + 4g = 80 \)
\( 40 + 4g = 80 \)
\( 4g = 80 - 40 = 40 \)
\( g = \frac{40}{4} = 10 \)

Answer:

The cost of one rose bush is \$5 and the cost of one geranium is \$10.