Respuesta :
Answer:
The cost of one rose bush is $5 and the cost of one shrub is $11.
Step-by-step explanation:
Given:
Ashley spent $228 on 6 rose bushes and 18 shrubs.
Heather spent $139 on 8 rose bushes and 9 shrubs.
Now, to find the cost of one rose bush and the cost of one shrub.
Let the cost of one rose bush be [tex]x.[/tex]
And let the cost of one shrub be [tex]y.[/tex]
So, the total money Ashley spent on 6 rose bushes and 18 shrubs:
[tex]6x+18y=228[/tex]
[tex]6x=228-18y[/tex]
Dividing both sides by 6 we get:
[tex]x=38-3y[/tex] .......(1)
Now, the total money Heather spent on 8 rose bushes and 9 shrubs are:
[tex]8x+9y=139[/tex]
Substituting the value of [tex]x[/tex] from equation (1) we get:
[tex]8(38-3y)+9y=139[/tex]
[tex]304-24y+9y=139[/tex]
[tex]304-15y=139[/tex]
Subtracting both sides by 304 we get:
[tex]-15y=-165[/tex]
Dividing both sides by -15 we get:
[tex]y=11.[/tex]
The cost of one shrub = $11.
Now, substituting the value of [tex]y[/tex] in equation (1) we get:
[tex]x=38-3y[/tex]
[tex]x=38-3\times 11[/tex]
[tex]x=38-33[/tex]
[tex]x=5.[/tex]
The cost of one rose bush = $5.
Therefore, the cost of one rose bush is $5 and the cost of one shrub is $11.
