Question

Darryl and DeShawn each improved their yards by planting rose bushes and ornamental grass. They bought their supplies from the same store. Darryl spent $143 on 11 rose bushes and 3 bunches of ornamental grass. DeShawn spent $132 on 11 rose bushes and 2 bunches of ornamental grass. What is the cost of one rose bush and the cost of one bunch of ornamental grass?

A) rose bush: $14, bunch of ornamental grass: $18
B) rose bush: $13, bunch of ornamental grass: $16
C) rose bush: $10, bunch of ornamental grass: $11
D) rose bush: $15, bunch of ornamental grass: $10

Answer 1

By setting up equations based on both Darryl's and DeShawn's purchases and solving for the cost of one rose bush and one bunch of ornamental grass, we find that a rose bush costs $10 and a bunch of ornamental grass costs $11.

Step-by-step explanation:

To solve this problem, we can set up two equations based on the costs that Darryl and DeShawn spent on rose bushes and ornamental grass. Let's designate r as the cost of one rose bush and g as the cost of one bunch of ornamental grass.

For Darryl, the equation based on his purchase is:

11r + 3g = $143

And for DeShawn, the equation for his purchase is:

11r + 2g = $132

To find the values of r and g, subtract the second equation from the first equation:

(11r + 3g) - (11r + 2g) = $143 - $132

This simplifies to:

g = $11

Now that we know the cost of one bunch of ornamental grass is $11, we can substitute this value into either of the original equations. Let's use DeShawn's purchase to find the cost of a rose bush:

11r + 2($11) = $132

11r + $22 = $132

11r = $110

r = $10

Therefore, the cost of one rose bush is $10 and the cost of one bunch of ornamental grass is $11.

The correct answer is C) rose bush: $10, bunch of ornamental grass: $11.