Shanice and mofor each improved their yards by planting rose bushes and shrubs. they bought their supplies from the same store. shanice spent $48 on 3 rose bushes and 6 shrubs. mofor spent $51 on 6 rose bushes and 3 shrubs. find the cost of one rose bush and the cost of one shrub.

Cost of one rose bush is $6 and the cost of one shrub is $5 .

Step-by-step explanation:

Let us assume that the cost of one rose bush be x .

Let us assume that the cost of one shrub be y .

As given

Shanice and mofor each improved their yards by planting rose bushes and shrubs.

They bought their supplies from the same store. Shanice spent $48 on 3 rose bushes and 6 shrubs.

Equations becomes

3x + 6y = 48

Mofor spent $51 on 6 rose bushes and 3 shrubs.

Equations becomes

6x + 3y = 51

Multiply 3x + 6y = 48 by 3 .

3 × 3x + 3 × 6y = 3 × 48

9x + 18y = 144

Multiply 6x + 3y = 51 by 6

6 × 6x + 6 × 3y = 6 × 51

36x + 18y = 306

Subtracted 9x + 18y = 144 from 36x + 18y = 306 .

36x - 9x + 18y - 18y = 306 - 144

27x = 162

x = 6

Putting the value of x in the equation 9x + 18y = 144 .

9 × 6 + 18y = 144

54 + 18y = 144

18y = 144 - 54

18y = 90

y = 5

Therefore the cost of one rose bush is $6 and the cost of one shrub is $5 .

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