Question

Ann calls her Swedish aunt 12 times a year. Her calls usually last between 20 minutes and 2 hours. Suppose AT&T charges $6.01 for a 7-minute call to Sweden and $6.79 for an 8-minute call to Sweden. Suppose that MCI charges $0.66 a minute plus a $1.99 overseas connection fee. a. Write a function that represents how much AT&T charges. Define your variables. b. Write a function that represents how much MCI charges. Use the same variable definitions as you did in part (a). c. Use an algebraic method (solve the two equations from parts (a) and (b) using substitution) to determine the length of a phone call that results in the same charge for both companies. ​

Answer 1

a. The function that represents how much AT&T charges is $6.01 + (x - 7) * $6.79 / 8 if x > 7, and $6.01 if 0 <= x <= 7. b. The function that represents how much MCI charges is $1.99 + $0.66x. c. To find the length of a phone call that results in the same charge for both companies, we set the two functions equal to each other and solve for x. The length of the call is approximately 1.38 minutes.

Step-by-step explanation:

a. The function that represents how much AT&T charges can be defined as follows:

Let x be the length of the phone call in minutes.
Then the total cost of the call is given by:

Cost = $6.01 + (x - 7) * $6.79 / 8 , if x > 7
Cost = $6.01, if 0 <= x <= 7

b. The function that represents how much MCI charges can be defined as follows:

Let x be the length of the phone call in minutes.
Then the total cost of the call is given by:

Cost = $1.99 + $0.66x

c. To determine the length of a phone call that results in the same charge for both companies, we can set the two functions equal to each other and solve for x:

$6.01 + (x - 7) * $6.79 / 8 = $1.99 + $0.66x
Simplifying the equation, we get:

x = 6.01 + (x - 7) * 0.84875 + 1.33x
Combining like terms and isolating x, we find:

0.15125x = 6.01 - 5.91875
x = 0.20875 / 0.15125
x ≈ 1.38 minutes