Question

use of the machine. the total cost, c, of making n copies at either store can be represented by an equation. write and graph a system to find how many copies you have to make for the cost to be the same at both stores. use pencil and paper. if you have to make a small number of copies which store should you go to? if you have to make a large number of copies which store should you go to? explain.

graph the system of equations. choose the correct answer below.

you have to make 5 copies for the cost to be the same at both stores.

Explanation:

Step1: Set costs equal to solve for $n$

Set the two cost equations equal:
$$10 = 0.60n + 1$$

Step2: Isolate the term with $n$

Subtract 1 from both sides:
$$10 - 1 = 0.60n$$
$$9 = 0.60n$$

Step3: Solve for $n$

Divide both sides by 0.60:
$$n = \frac{9}{0.60} = 15$$

Step4: Analyze small copy count (n=5)

Calculate cost for Store W: $c=10$
Calculate cost for Store Z: $c=0.60(5)+1=3+1=4$

Step5: Analyze large copy count (n>15, e.g. n=20)

Calculate cost for Store W: $c=10$
Calculate cost for Store Z: $c=0.60(20)+1=12+1=13$

Step6: Match equations to graph

Store W: $c=10$ (horizontal line, y-intercept 10)
Store Z: $c=0.60n+1$ (line with slope 0.6, y-intercept 1), intersecting at $n=15, c=10$. This matches Graph A.

Answer:

1. Number of copies for equal cost: 15
2. Small number of copies (e.g., 5): Choose Store Z (lower cost: $4 vs. $10 at Store W)
3. Large number of copies (e.g., 20): Choose Store W (lower cost: $10 vs. $13 at Store Z)
4. Correct graph: Option A
5. Correct equation pair: Option B (Store W: $c=10$; Store Z: $c=0.60n+1$)