Question

1. shawna and mark each improved their yards by planting rose bushes and ornamental grass. they bought their supplies from the same store. shawna spent $16 on 1 rose bush and 6 bunches of ornamental grass. mark spent $36 on 4 rose bushes and 10 bunches of ornamental grass. what is 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 and \( g \) be the cost of one bunch of ornamental grass.

Step2: Set Up Equations

From Shawna's purchase: \( r + 6g = 16 \)
From Mark's purchase: \( 4r + 10g = 36 \)

Step3: Solve the System of Equations

First, multiply the first equation by 4: \( 4r + 24g = 64 \)
Subtract the second equation from this new equation:
\( (4r + 24g) - (4r + 10g) = 64 - 36 \)
\( 14g = 28 \)
\( g = 2 \)
Substitute \( g = 2 \) into the first equation: \( r + 6(2) = 16 \)
\( r + 12 = 16 \)
\( r = 4 \)

Answer:

The cost of one rose bush is $4 and the cost of one bunch of ornamental grass is $2.