Question

A landscaping company has two orders for bushes and trees.

Order 1 for 12 bushes and 15 trees that will cost the customer $600
Order 2 for 8 bushes and 20 trees that will cost the customer $680
What is the cost of one bush?

Answer 1

First, choose a variable to represent the number of bushes, and another variable to represent the number of trees.

Answer 2

Let the cost of 1 bush be x and the cost of 1 tree be y.

"12 bushes and 15 trees that will cost the customer $600"
12x + 15y = 600 ----- (1)

"8 bushes and 20 trees that will cost the customer $680"
8x + 20y = 680 ------ (2)

Eliminate y from (1) and (2) and solve for x.

Answer 3

Thank you.

Answer 4

You are welcome.

Answer 5

Wait. so the answer is..?

Answer 6

12x + 15y = 600 ----- (1)
This can be simplified by dividing by 3:
4x + 5y = 200

8x + 20y = 680 ------ (2)
This can be simplified by dividing by 4:
2x + 5y = 170

So we have:
4x + 5y = 200
2x + 5y = 170
To eliminate y, subtract the two equations. What do you get?

Answer 7

If you subtract the two equations, the 5y will cancel and you get
2x = 30
x = 15

So the price of one bush = $15.

Answer 8

Thank you so much.

Answer 9

You are welcome.