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: $10 , shrub: $4. rose bush: $7 , shrub: $5. rose bush: $13 , shrub: $2. PLS HELP WILL MARK BRAINLIEST

To solve this, start by writing equations for what each spent. Use x for the cost of a rose bush and y for the cost of a shrub. Below would be the equations for each.

Rob: 8x + 5y = 100

Amy: 8x + 8y = 112

Now to find the cost, we multiply Rob's equation by -1 and add them together. This will get x to cancel and allow us to solve for y.

-8x - 5y = -100

8x + 8y = 112

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3y = 12

y = 4

So we know the cost of a shrub is $4. Now we can plug that in to either of the original equations and solve for the rose bush cost.

8x + 5y = 100

8x + 5(4) = 100

8x + 20 = 100

8x = 80

x = 10

Which means that a rose bush costs $10.