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,**