Question

Ashley spent $228 on 6 rose bushes and 18 shrubs. Heather spent $139 on 8 rose bushes and 9 shrubs. What is the cost of one rose bush and the cost of one shrub?

Answer 1

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 $x.$

And let the cost of one shrub be $y.$

So, the total money Ashley spent on 6 rose bushes and 18 shrubs:

$6x+18y=228$

$6x=228-18y$

Dividing both sides by 6 we get:

$x=38-3y$   .......(1)

Now, the total money Heather spent on 8 rose bushes and 9 shrubs are:

$8x+9y=139$

Substituting the value of $x$ from equation (1) we get:

$8(38-3y)+9y=139$

$304-24y+9y=139$

$304-15y=139$

Subtracting both sides by 304 we get:

$-15y=-165$

Dividing both sides by -15 we get:

$y=11.$

The cost of one shrub = $11.

Now, substituting the value of $y$ in equation (1) we get:

$x=38-3y$

$x=38-3\times 11$

$x=38-33$

$x=5.$

The cost of one rose bush = $5.

Therefore, the cost of one rose bush is $5 and the cost of one shrub is $11.