## 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 th

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?

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3 months 2022-02-17T15:19:39+00:00 1 Answer 0 views 0

1. 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.