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Question

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.