Heather and Amanda each improved their yards by planting rose bushes and geraniums. They bought their supplies from the same storm. Heather spent $50 on 2 rose bushes and 3 geraniums. Amanda spent $186 on y rose bushes and 12 geraniums. What is the cost of one bush and one geranium?

one Bush costs $19 and one geranium costs $6

Step-by-step explanation:

Let the cost of one Bush be x

Let the cost of one geranium be y

If Heather spent $50 on 2 rose bushes and 3 geraniums, then the equation that represent the statement is:

2x+3y = 50… 1

If amanda spent $186 on 6 rose bushes and 12 geraniums, then the equation representation will be:

6x+12y = 186…2

Solve equations 1 and 2 simultaneously

2x+3y = 56 1 × 3

6x+12y = 186 2 × 1

…

6x+9y = 168

6x+12y = 186

Subtract

9y - 12y = 168-186

-3y = -18

y = -18/-3

y = 6

Substitute y = 6 into equation 1:

2x+3y = 56

2x+3(6) = 56

2x+18 = 56

2x = 56-18

2x = 38

x = 38/2

x = 19

Hence one Bush costs $19 and one geranium costs $6

NB: note that the y rose bushes in the question was corrected and 6 rose bushes was used instead in the equation.

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