Shreya and beth each improved their yards by planting rose bushes and ornamental grass. They brought their supplies from the same store. Shreya spent $68 on 4 rose bushes and 4 bunches of ornamental grass. Beth spent $115 on 11 rose bushes and 2 bunches of ornaments grass. What is the cost of one rose bush and the cost on one bu bunch ornamental grass

The cost of one rose bush is $ 9 and the cost on one bunch pf ornamental grass is $ 8.

Explanation:

Name the variables and build a system of two equations with two unknowns.

1. Variable r: cost of one rose bush

2. Variable g: cost of one bunch of ornamental grass.

3. First equation:

Shreya spent $68 on 4 rose bushes and 4 bunches of ornamental grass.

4r + 4g = 68

4. Second equation:

Beth spent $115 on 11 rose bushes and 2 bunches of ornaments grass.

11r + 2g = 115

5. System of equations:

4r + 4 g = 68 equation 1 11r + 2g = 115 equation 2

6. Solve the system

a) Divide the equation 1 by 2:

2r + 2g = 34 equation 1a 11r + 2g = 115 equation 2

b) Subtract equation 1a from equation 2:

11r - 2r = 115 - 34 9r = 81 r = 81 / 9 r = 9

c) Substitute the value of r into the equation 1a:

2 (9) + 2g = 34 9 + g = 17 g = 17 - 9 g = 8

7. Conclusion:

The cost of one rose bush is $ 9 and the cost on one bunch pf ornamental grass is $ 8.