John and Kathleen each improved their yards planting rose bushes and shrubs . They bought their supplies from the same store. John spent $228 on 12.rose bushes and 11 shrubs. Kathleen spent $108,on 6 rose bushes and 5 shrubs. Find the cost of one rose bush and the cost of one shrub.

Question

John and Kathleen each improved their yards planting rose bushes and shrubs . They bought their supplies from the same store. John spent $228 on 12.rose bushes and 11 shrubs. Kathleen spent $108,on 6 rose bushes and 5 shrubs. Find the cost of one rose bush and the cost of one shrub.

Set up and solve a system of equations

Answer 1

12r+11s = 228

6r+5s = 108

...

Answer 2

To find the cost of one rose bush and one shrub, we can set up a system of equations using the given information.

Let's represent the cost of one rose bush as 'x' and the cost of one shrub as 'y'.

According to the problem, John spent $228 on 12 rose bushes and 11 shrubs. So, the equation for John's spending can be written as:

12x + 11y = 228 ----(1)

Similarly, Kathleen spent $108 on 6 rose bushes and 5 shrubs. So, the equation for Kathleen's spending can be written as:

6x + 5y = 108 ----(2)

Now, we have a system of equations:

12x + 11y = 228 ----(1)
6x + 5y = 108 ----(2)

To solve this system of equations, we can use one of the methods such as substitution or elimination.

We'll use the elimination method to solve the system:

Multiplying equation (2) by 2, we get:

12x + 10y = 216 ----(3)

Now subtract equation (3) from equation (1):

(12x + 11y) - (12x + 10y) = 228 - 216
y = 12

Now, substitute the value of y back into equation (2) to find x:

6x + 5(12) = 108
6x + 60 = 108
6x = 108 - 60
6x = 48
x = 8

So, the cost of one rose bush is $8 and the cost of one shrub is $12.