Question

or
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

Fred wrote a business plan for an entrepreneurship class, and now he has to make bound copies. Fred could use a printer who charges a setup fee of $45 and $6 for every copy printed. Another possibility is to go to the office supply store, where he could pay an up-front fee of $28 and $7 per copy. There is a certain number of copies that makes the two options equivalent in terms of cost. How many copies is that? How much would the copies cost?


For
copies, the cost is $
.

Answer 1

Let's denote the number of copies Fred wants to make as \( x \). We can set up a system of equations based on the costs of each option.

1. **Cost for the printer**:
\[
C_1 = 45 + 6x
\]
where \( C_1 \) is the total cost when using the printer.

2. **Cost for the office supply store**:
\[
C_2 = 28 + 7x
\]
where \( C_2 \) is the total cost when using the office supply store.

To find the number of copies that make the costs equivalent, we can set up the equation:
\[
45 + 6x = 28 + 7x
\]

Now, let's solve for \( x \).

First, subtract \( 6x \) from both sides:
\[
45 = 28 + x
\]

Next, subtract 28 from both sides:
\[
45 - 28 = x
\]
\[
17 = x
\]

Now, we know that \( x = 17 \). This means that the two options will cost the same when Fred makes 17 copies.

Next, we can calculate the cost for either option when \( x = 17 \). We'll use the printer's cost equation:
\[
C_1 = 45 + 6(17)
\]
\[
C_1 = 45 + 102
\]
\[
C_1 = 147
\]

Thus, the two options are equivalent when Fred makes **17 copies**, and the cost would be **$147**.

Filling in the blanks, we have:

For **17** copies, the cost is **$147**.