Question

Rob and Amy each improved their yards by planting rose bushes and shrubs. They bought their supplies from the same store. Rob spent $100 on 8 rose bushes and 5 shrubs. Amy spent $112 on 8 rose bushes and 8 shrubs. What is the cost of one rose bush and the cost of one shrub?

rose bush: $15 , shrub: $5

rose bush: $13 , shrub: $2

rose bush: $10 , shrub: $4

rose bush: $7 , shrub: $5

Answer 1

The cost of one rose bushes be $10 and the cost of shrubs $4.

Step-by-step explanation

Let us assume that the cost of rose bushes be x .

Let us assume that the cost of shrubs be y .

As given

Rob and Amy each improved their yards by planting rose bushes and shrubs.

They bought their supplies from the same store.

Rob spent $100 on 8 rose bushes and 5 shrubs.

Than the equation

8x + 5y = 100

Amy spent $112 on 8 rose bushes and 8 shrubs.

8x + 8y = 112

Than the two equation

8x + 5y = 100 and 8x + 8y = 112

Subtracting 8x + 5y = 100 from 8x + 8y = 112

8x - 8x + 8y - 5y = 112 - 100

3y = 12

`y = (12)/(3)`

y = $4

Put in the equation 8x + 5y = 100 .

8x + 5 × 4 = 100

8x + 20 = 100

8x = 100 - 20

8x = 80

`x = (80)/(8)`

x = $10

Therefore the cost of one rose bushes be $10 and the cost of shrubs $4.