Question

1. jennifer sells necklaces for $30 for each necklace. to make the necklaces, she buys supplies from an online store at a cost $15 per necklace. the company charges her a flat shipping fee of $50. a) write a system of equations to represent this situation (one equation for expenses and one for income): b) graph (a graph with x - axis labeled number of necklaces and y - axis labeled dollars) c) how many necklaces would she have to sell to make a profit?

Explanation:

Step1: Define variables

Let $x$ = number of necklaces, $y$ = total dollars.

Step2: Write expense equation

Expenses = flat fee + per-unit cost: $y = 15x + 50$

Step3: Write income equation

Income = price per necklace × quantity: $y = 30x$

Step4: Find break-even point

Set income = expenses:
$$30x = 15x + 50$$
Subtract $15x$ from both sides:
$$15x = 50$$
Solve for $x$:
$$x = \frac{50}{15} \approx 3.33$$

Step5: Determine profit threshold

Since necklaces are whole units, sell 4+ to profit.

Answer:

a) Expenses: $y = 15x + 50$; Income: $y = 30x$
b) (Graph details:

• For $y=30x$: Plot points (0,0), (1,30), (2,60), (3,90), (4,120) and draw a line through them.
• For $y=15x+50$: Plot points (0,50), (1,65), (2,80), (3,95), (4,110) and draw a line through them. The lines intersect near $x\approx3.33$)

c) 4 necklaces