You decide to enroll in a plan that gives you a 10% discount if you make telephone calls between 7:00 p.m. and 6:00 a.m. The per minute charge is $0.10 and the sales tax is 6%. On the first month’s bill you used the phone for 130 minutes between 6:00 a.m. and 7:00 p.m. and then for 400 minutes between 7:00 p.m. and 6:00 a.m. How much was your total bill?

Question

(1 point)
Responses

$56.18
$56.18

$53.00
$53.00

$51.94
$51.94

$49.00

Answer 1

To calculate the total bill, we need to break it down into two parts: the charges for calls made during the day (6:00 a.m. to 7:00 p.m.) and the charges for calls made at night (7:00 p.m. to 6:00 a.m.).

1. Daytime Charges:

   • Minutes used: 130 minutes
   • Rate: $0.10 per minute
   • Total for daytime calls: \[ 130 , \text{minutes} \times 0.10 , \text{dollars/minute} = 13.00 , \text{dollars} \]

2. Nighttime Charges:

   • Minutes used: 400 minutes
   • Rate: $0.10 per minute
   • Total for nighttime calls before discount: \[ 400 , \text{minutes} \times 0.10 , \text{dollars/minute} = 40.00 , \text{dollars} \]
   • Discount (10%): \[ 10% , \text{of} , 40.00 , \text{dollars} = 4.00 , \text{dollars} \]
   • Total for nighttime calls after discount: \[ 40.00 , \text{dollars} - 4.00 , \text{dollars} = 36.00 , \text{dollars} \]

3. Total Charges Before Tax:

   • Total charges = Daytime charges + Nighttime charges: \[ 13.00 , \text{dollars} + 36.00 , \text{dollars} = 49.00 , \text{dollars} \]

4. Sales Tax:

   • Sales tax: 6%
   • Total tax amount: \[ 6% , \text{of} , 49.00 , \text{dollars} = 0.06 \times 49.00 = 2.94 , \text{dollars} \]

5. Total Bill:

   • Total bill = Total charges + Sales tax: \[ 49.00 , \text{dollars} + 2.94 , \text{dollars} = 51.94 , \text{dollars} \]

Thus, the total bill is $51.94. Therefore, the correct response is:

$51.94