Q. 22 - Precalculus Enhanced with Graphing Utilities

Question

Comparing Phone Companies Marissa must decide

between one of two companies as her long-distance phone

provider. Company A charges a monthly fee of \(7.00 plus

\)0.06 per minute, while Company B does not have a monthly

fee, but charges $0.08 per minute.

(a) Find a linear function that relates cost, C, to total

minutes on the phone, x, for each company.

(b) Determine the number of minutes x for which the bill

from Company A will equal the bill from Company B.

(c) Over what interval of minutes x will the bill from

Company B be less than the bill from Company A?

Step-by-Step Solution

Answer

(a) Total cost for A, $C=0.06x+7$

Total cost for B, $C=0.08x$

(b) $x=350$ minute

(c) The interval is $[0,350]$.

Part (a) Step 1. Given Information

The monthly fee and charges of company A is $\$7.00 \& \$0.06$\mint.

The monthly fee and charges of company B $\$0 \& \$0.08$\mint.

Part (a) Step 2. Calculation

 By the given information, the total cost for A is, $C=0.06x+7$

By the given information, the total cost for B is, $C=0.08x$

 

Part (b) Step 1. Given Information

The monthly fee and charges of company A is $\$7.00 \& \$0.06$\mint.

The monthly fee and charges of company B $\$0.00 \& \$0.08$\mint.

Part (b) Step 2. Calculation

According to problem 

$0.06x+7=0.08x$

Therefore, $x=350$mints

Part (c) Step 1. Given Information

The monthly fee and charges of company A is $\$7.00 \& \$0.06$\mint.

The monthly fee and charges of company B $\$0.00 \& \$0.08$\mint.

Part (c) Step 2. Calculation

The charges will be equal for both companies at $x=350$mint.

Hence 

Over the interval $[0,350]$ of minutes the bill from

Company B is less than the bill from Company A.