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: $7 , shrub: $5 rose bush: $15 , shrub: $5 rose bush: $13 , shrub: $2 rose bush: $10 , shrub: $4 HELPPP ASAAPPP

Answer 1

Cost of one rose bush: $10

Cost of one shrub: $4

Explanation:

1. You must make a system of equation, where
`x` is the cost of one rose bush and
`y` is the cost of one shrub.

2. You know that Rob spent $100 on 8 rose bushes and 5 shrubs and Amy spent $112 on 8 rose bushes and 8 shrubs, therefore, you have.

`\left \{ {{8x+5y=100} \atop {8x+8y=112}} \right.`

3. Apply the Substitution method. Multiply the first equation by -1, add both equations and solve for y:

`\left \{ {{8x-5y=-100}\atop {8x+8y=112}} \right.\\------\\3y=12\\y=4`

4. Substitute y into one of the equation and solve for x:

`8x+5(4)=100\\8x=80\\x=10`