High School

Castel and Kali each improved their yards by planting rose bushes and geraniums. They brought their supplies from the same store. Castel spent $115 on 5 rose bushes and 12 geraniums. Kail spent $94 on 10 rose bushes and 8 geraniums.


(a) Write a system of equations that represents the scenario


(b) Solve the system to determine the cost of one rose bush and the cost of one geraniums.

Castel and Kali each improved their yards by planting rose bushes and geraniums They brought their supplies from the same store Castel spent 115 on

Answer :

a) The system of equations that represents the scenario is given as follows:

  • 5x + 12y = 115.
  • 10x + 8y = 94.

b) The costs are given as follows:

  • One bush: $2.6.
  • One geranium: 8.5.

How to define the system of equations?

The variables for the system of equations are defined as follows:

  • Variable x: cost of a bush.
  • Variable y: cost of a geranium;

Castel spent $115 on 5 rose bushes and 12 geraniums, hence:

5x + 12y = 115.

Kail spent $94 on 10 rose bushes and 8 geraniums, hence:

10x + 8y = 94

Then the system is defined as follows:

  • 5x + 12y = 115.
  • 10x + 8y = 94.

Multiplying the first equation by 2 and subtracting by the second, we have that the value of y is obtained as follows:

24y - 8y = 230 - 94

16y = 136

y = 136/16

y = 8.5.

Then the value of x is obtained as follows:

5x + 12(8.5) = 115

x = (115 - 12 x 8.5)/5

x = 2.6.

More can be learned about a system of equations at https://brainly.com/question/13729904

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