Threse are two questions and two answers:

Question 1. The school band sells carnations on Valentine’s Day for $2 each. They buy the carnations from a florist for $0.50 each, plus a $16 delivery charge.

a. Write a system of equations to describe the situation.

Answer:

1) Sale:

Each carnation at $2 ⇒ y = 2x

2) Cost:

Fixed cost + variable cost = deliver charge + unit cost × number of carnations ⇒

y = 0.5x + 16

∴ System of equations:

y = 2x; y = 0.50x + 16. ← answer

b. Graph the system. What does the solution represent?

(Which x-values should I choose to graph the equations above so that they intersect?)

Answer:

The solution represents the number of carnations for which the cost and the sale are equals (zero profit).

You can use the values of this table

x —– Sale = 2x ——– 0.5x + 16

0 ——- 0 ————— 16

2 —— 4 —————- 1 + 16 = 17

4 —— 8 ————— 2 + 16 = 18

6 —— 12 ————– 3 + 16 = 19

8 —— 16 ————– 4 + 16 = 20

10 —— 20 ———— 5 + 16 = 21

12 —– 24 ———— 6 + 16 = 22

Then, the solution is between 10 and 12 carnations.

Indeed it is: 2x = 0.5x + 16 ⇒ 1.5x = 16 ⇒ x = 16 / 1.5 = 10.67

Therefore, choose values of x that include the interval [0, 12].

c. Explain whether the solution shown on the graph makes sense in this situation. If not, give a reasonable solution.

The exact solution is x = 10.67, which is not a real solution, since the number of carnations must be integer.

The most reasonable solution is the next integer, i.e. 11.

Question 2. 6(x + 2) = -2(x + 10)

1) Expand using distributive property:

6x + 12 = -2x – 20

2) Addition and subtraction property of equality:

6x + 2x = – 20 – 12

3) Combine like terms:

8x = – 32

4) Division property of equality:

x = – 32 / 8 = – 4 ← answer,