A cell phone plan costs each month, plus ¢ per text message sent, plus ¢ for each minute used over hours. In January Michelle sent text messages and talked for hours. How much did she have to pay?
- A)
$ 24.00
- B)
$ 24.50
- C)
$ 25.50
- D)
$ 28.00
- E)
$ 30.00
Answer
D
Key insight
Only the half hour beyond 30 hours is billed, and it must be converted to 30 minutes at 10 cents each before adding the text charge.
Solution
Add the three parts of the bill separately.
Fixed charge: .
Texts: messages at cents each is cents, or .
Overage: Michelle talked hours beyond the free allowance, and hours is minutes. At cents per minute that is cents, or .
Total: dollars.
The answer is .
Why this works
A bill with a base fee plus per-unit charges is just a sum of products, but every product must use matching units: cents versus dollars, and minutes versus hours. Convert each piece into the same unit before adding. When a plan says "over hours," only the excess is billed, so subtract the allowance first.
The trap
Treating the extra 0.5 hours as 0.5 minutes (or as half a dollar) instead of 30 minutes, giving a total near 24.50 or 25.50.
Common mistakes
- Treating the extra 0.5 hours as 0.5 minutes (or as half a dollar) instead of 30 minutes, giving a total near 24.50 or 25.50.
- Billing all hours at cents per minute instead of only the half hour over the limit.
- Adding cents and cents as if they were dollars.
Techniques
Set up the equation/formula and compute; no special trick needed