Question

Darci placed two orders for flowers and bushes. The first order was for 24 flowers and 6 bushes. The total of the first order was $144. The second order was for 18 flowers and 3 bushes. The total of the second order was $90. Write a system of equations to represent this situation. Then solve the system of equations by substitution. Explain what the solution means.

Answer 1

See below.

Explanation:

Let f = cost of one flower, and let b = cost of one bush.

First order:

24f + 6b = 144

Second order:

18f + 3b = 90

We have a system of two equations in two unknowns.

24f + 6b = 144

18f + 3b = 90

The first equation is divisible by 6, so let's divide both sides of the first equation by 6. The second equation is divisible by 3, so let's divide both sides of the second equation by 3.

4f + b = 24

6f + b = 30

To solve by substitution, we solve the first equation for b.

b = 24 - 4f

Now we substitute b in the second equation with 24 - 4f.

6f + 24 - 4f = 30

2f + 24 = 30

2f = 6

f = 3

Now we substitute 3 for f in the equation above that is solved for b.

b = 24 - 4(3)

b = 24 - 12

b = 12

f = 3 means the price of one flower is $3.

b = 12 means the price of one bush is $12.