Question
An online fax company, EFaxdt.com, has a customer plan where a subscriber pays a monthly subscription fee of \( \$ 18.5 \) dollars and can send/receive 80 fax pages at no additional cost. For each page sent or received past the 80 page limit, the customer must pay an overage fee of 50.06 per page. The following expression gives the total cost, in dollars, to send \( p \) pages beyond the plan's monthly limit. \( C=0.06 p+18.5 \) If the monthly bill under this plan comes out to be \( \$ 21.5 \), what was the total number of pages that were sent or received? Answer: The total number of pages sent/received was Next Question
Ask by Patel Cummings. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The total number of pages sent or received was 130.
Solution
Let \( p \) denote the number of extra pages sent/received beyond the 80-page limit. The total cost is given by
\[
C = 0.06p + 18.5.
\]
Given that the total bill is \( \$21.5 \), we have
\[
0.06p + 18.5 = 21.5.
\]
**Step 1:** Subtract \( 18.5 \) from both sides:
\[
0.06p = 21.5 - 18.5 = 3.
\]
**Step 2:** Solve for \( p \) by dividing both sides by \( 0.06 \):
\[
p = \frac{3}{0.06} = 50.
\]
This means \( 50 \) pages were sent/received beyond the monthly limit.
**Step 3:** Add the included \( 80 \) pages to the extra \( 50 \) pages to find the total number of pages:
\[
\text{Total pages} = 80 + 50 = 130.
\]
Thus, the total number of pages sent/received was \( 130 \).
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Bonus Knowledge
To find the total number of pages sent or received, we first look at the total cost formula given, \( C = 0.06p + 18.5 \). We know the total cost was \( 21.5 \). So, we set up the equation: \[ 21.5 = 0.06p + 18.5 \] Subtract \( 18.5 \) from both sides: \[ 21.5 - 18.5 = 0.06p \] \[ 3 = 0.06p \] Now, divide both sides by \( 0.06 \): \[ p = \frac{3}{0.06} \] \[ p = 50 \] Now, add this to the initial 80 pages included in the plan: Total pages = \( 80 + 50 = 130 \). So, the total number of pages sent or received was **130 pages**.