Question

rob and micaela each improved their yards by planting rose bushes and ornamental grass. they bought their supplies from the same store. rob spent $66 on 7 rose bushes and 2 bunches of ornamental grass. micaela spent $71 on 7 rose bushes and 3 bunches of ornamental grass. find the cost of one rose bush and the cost of one bunch of ornamental grass.

Explanation:

Step1: Define variables

Let \( r \) be the cost of one rose bush (in dollars) and \( g \) be the cost of one bunch of ornamental grass (in dollars).

Step2: Set up equations

From Rob's purchase: \( 7r + 2g = 66 \)
From Micaela's purchase: \( 7r + 3g = 71 \)

Step3: Subtract equations to eliminate \( r \)

Subtract the first equation from the second:
\( (7r + 3g) - (7r + 2g) = 71 - 66 \)
Simplify: \( g = 5 \)

Step4: Substitute \( g = 5 \) into first equation

\( 7r + 2(5) = 66 \)
\( 7r + 10 = 66 \)
Subtract 10: \( 7r = 56 \)
Divide by 7: \( r = 8 \)

Answer:

The cost of one rose bush is \$8 and the cost of one bunch of ornamental grass is \$5.