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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

Respuesta :

Edufirst

Answer:

  • 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.

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