Question

Jack placed two orders with a local nursery. The first order was for 13 rose bushes and 4 miniature orchid plants. This order totaled $500. The second order was for 2 rose bushes and 1 miniature orchid. This order totaled $100. The receipts do not list the price per plant, and Jack would like to know how much each plant cost. This system of equations represents the situation. 13x + 4y = 500 2x + y = 100 In the equations, x represents the cost of each rose bush and y represents the cost of each orchid plant. The graph of this system is shown below. How much does each type of plant cost? The price of each rose bush is $, and the price of each orchid is $.

Answer 1

Hi!

The two equations,
Equation A: 13x + 4y = 500
Equation B: 2x + y = 100

Whatever we do to an equation, we have to do it to both sides.

We need to isolate y on one side in equation B, by subtracting 2x from both sides.
2x - 2x + y = 100 - 2x
y = 100 - 2x
Put the value of y into equation A.
13x + 4(100 - 2x) = 500
Simplify the equation with the distribution property.
4 · 100 = 400
4 · -2x = -8x
13x + 400 - 8x = 500
Continue simplifying
13x - 8x = 5x
5x + 400 = 500
Subtract 400 from both sides
5x + 400 - 400 = 500 - 400
5x = 100
Divide by 5 on both sides.
5x/5 = 100/5
x = 20
Put the value of x into equation B.
2 · 20 + y = 100
Simplify
40 + y = 100
Subtract 40 from both sides
40 - 40 + y = 100 - 40
y = 60

x = 20
y = 60

Let's check our answer by putting the values in both equations.

13 · 20 + 4 · 60 = 500
260 + 240 = 500
500 = 500

2 · 20 + 60 = 100
40 + 60 = 100
100 = 100

The answer is
$20 per rose bush
$60 per orchid plant

Hope this helps! :)