Question

reasoning the cost of making copies at store w is $10 regardless of the number of copies. the cost of making copies at store z is 60¢ per copy plus a $1 charge for the 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. write the system of equations. choose the correct answer below. a. store w c = 0.60n - 10 store z c = 1 b. store w c = 10 store z c = 0.60n + 1 c. store w c = 0.60n + 1 store z c = 10 d. store w c = 10 store z c = 0.60n - 1

Explanation:

Step1: Define Store W's cost

$c = 10$

Step2: Define Store Z's cost

$c = 0.60n + 1$

Step3: Find break-even number of copies

Set $10 = 0.60n + 1$
Subtract 1 from both sides: $9 = 0.60n$
Solve for $n$: $n = \frac{9}{0.60} = 15$

Step4: Analyze small/large copy counts

For $n < 15$ (small copies): Compare costs. For $n=1$, Store Z: $c=0.60(1)+1=1.60 < 10$. For $n > 15$ (large copies): For $n=20$, Store Z: $c=0.60(20)+1=13 > 10$.

Answer:

Correct system of equations: B. Store W: $c=10$; Store Z: $c=0.60n+1$

• For a small number of copies ($n < 15$), choose Store Z, as its total cost is lower.
• For a large number of copies ($n > 15$), choose Store W, as its fixed $10 cost is lower than Store Z's variable cost.
• At $n=15$ copies, the cost is $10 at both stores.