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Chapter 8: Problem 4

Your Sprint Basic cell phone rate plan costs 29.99 dollars a month plus 45 cents per minute for every minute over 200 minutes during the month. a. Write a verbal rule to determine the total monthly cost for your cell phone, assuming you go over 200 minutes. b. Translate the verbal rule in part a into an equation using \(c\) to represent the total monthly cost and \(n\) to represent the overage minutes for the month. c. Determine the monthly cost for 250 overage minutes. d. If your total bill for the month was 61.49 dollars, how many overage minutes did you have?

Short Answer

Expert verified
Answer: The total monthly cost for a Sprint Basic cell phone rate plan with 250 overage minutes is 142.49 dollars, and a person had 70 overage minutes if their total bill for the month was 61.49 dollars.

Step by step solution

01

Writing a verbal rule

The total monthly cost of the cell phone bill is 29.99 dollars plus 45 cents multiplied by the number of overage minutes.
02

Translating the verbal rule into an equation

Let \(c\) represent the total monthly cost and \(n\) represent the number of overage minutes. The equation representing the relationship is: \(c = 29.99 + 0.45n\)
03

Determine the monthly cost for 250 overage minutes

We need to find the total monthly cost when \(n = 250\). Substitute \(n = 250\) into the equation: \(c = 29.99 + 0.45(250)\). Now solve for \(c\): \(c = 29.99 + 112.50 = 142.49\) The total monthly cost for 250 overage minutes will be 142.49 dollars.
04

Find the number of overage minutes if the total bill for the month was 61.49 dollars

We know the total bill for the month, which is 61.49 dollars. We need to find the overage minutes used (\(n\)) based on this bill. We can use the same equation as before to solve for \(n\). Set \(c = 61.49\) and solve for n: \(61.49 = 29.99 + 0.45n\) Now solve for \(n\): \(31.50 = 0.45n\) \(n = \dfrac{31.50}{0.45} = 70\) The person had 70 overage minutes during the month.

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