A store that offers faxing services charges, a fixed amount to fax one page and a different amount for faxing each additional page. If the cost of faxing 5 pages is $3.05 and the cost of faxing 13 pages is $6.65.
a. What is the cost of faxing one page?
b. What is the total cost of faxing three pages to the same telephone number?

Answer

To solve the problem step by step, we will define the variables and set up equations based on the information given.

### Step 1: Define Variables
Let:
- \( x \) = the fixed cost to fax one page (in dollars)
- \( y \) = the additional cost for each additional page (in dollars)

### Step 2: Set Up Equations
From the question, we know:
1. The cost to fax 5 pages is $3.05.
- This can be expressed as:
\[ x + 4y = 3.05 \quad \text{(Equation 1)} \]
(Here, \( 4y \) accounts for the additional 4 pages.)

2. The cost to fax 13 pages is $6.65.
- This can be expressed as:
\[ x + 12y = 6.65 \quad \text{(Equation 2)} \]
(Here, \( 12y \) accounts for the additional 12 pages.)

### Step 3: Solve the Equations
To eliminate \( x \), we can subtract Equation 1 from Equation 2:
\[ (x + 12y) - (x + 4y) = 6.65 - 3.05 \]
This simplifies to:
\[ 12y - 4y = 3.60 \]
\[ 8y = 3.60 \]
Now, divide both sides by 8:
\[ y = \frac{3.60}{8} = 0.45 \]

### Step 4: Substitute \( y \) Back to Find \( x \)
Now that we have \( y \), we can substitute it back into Equation 1 to find \( x \):
\[ x + 4(0.45) = 3.05 \]
\[ x + 1.80 = 3.05 \]
Subtract 1.80 from both sides:
\[ x = 3.05 - 1.80 = 1.25 \]

### Step 5: Answer Part (a)
The cost of faxing one page is:
\[ \boxed{1.25} \]

### Step 6: Calculate the Cost of Faxing 3 Pages (Part b)
To find the cost of faxing 3 pages, we use the formula:
\[ \text{Total Cost} = x + (3 - 1)y \]
Substituting the values of \( x \) and \( y \):
\[ \text{Total Cost} = 1.25 + (2)(0.45) \]
Calculating the additional cost:
\[ \text{Total Cost} = 1.25 + 0.90 = 2.15 \]

### Step 7: Answer Part (b)
The total cost of faxing three pages is:
\[ \boxed{2.15} \]