Question

Calls on a particular pay telephone are charged according to this rule: Charge 25 cents for the call, plus 10 cents for every 3 minutes, or part of 3 minutes, after the first 3 minutes. a. How much would it cost you to make a 10 -minute call? b. If you have \(\$ 1.15\) in change, how long can you talk if you make a single call?

Short answer

10-minute call costs 55 cents. With \)1.15 in change, you can talk for 30 minutes.

Step-by-step solution

Understand the Charge Rule

The rule states that the initial 3 minutes cost 25 cents, and every additional 3 minutes or part of 3 minutes cost 10 cents.

Calculate Cost for 10-minute Call - Part a

First 3 minutes cost 25 cents. The remaining time is 10 - 3 = 7 minutes. For the next 7 minutes, divide by 3 to get parts of 3 minutes: 7/3 = 2 parts with remainder. So, it would be 3 parts in total. Each part costs 10 cents. Thus, 3 * 10 = 30 cents. Total cost: 25 + 30 = 55 cents.

Determine Maximum Call Duration with \(1.15 - Part b

First, convert \)1.15 to cents: \(1.15 = 115 cents. Subtract the initial 25 cents, leaving 115 - 25 = 90 cents. Each part of 3 minutes costs 10 cents: 90 / 10 = 9 parts. Each part represents 3 minutes: 9 * 3 = 27 minutes. Adding the first 3 minutes: 27 + 3 = 30 minutes.

Key concepts

cost calculation

Understanding how charges are calculated for calls made from a pay telephone is essential to solving the given problem. The charge rule in this case is straightforward: the first 3 minutes cost 25 cents, and every additional period of up to 3 minutes costs another 10 cents. This means:

• First 3 minutes = 25 cents
• Each additional 3-minute period (or part thereof) = 10 cents

So, if you make a 10-minute call, you first subtract the initial 3 minutes, leaving you with 7 minutes. Since every 3-minute period or part thereof after the initial 3 minutes costs 10 cents, you need to calculate how many such periods you have. In this case, there are two full periods and a partial period, making 3 periods in total. Multiply 3 by 10 cents to get 30 cents. Add this to the initial 25 cents to get a total of 55 cents for a 10-minute call.

time division

Dividing time into segments based on the given charge intervals is key. In this exercise, you calculate costs based on segments of 3 minutes after the first 3 minutes. Here's the process:

• Determine how much time remains after subtracting the initial 3 minutes.
• Divide this time by 3 to find out how many segments you have.
• If there is any remaining time, count this as an additional segment since even a partial 3-minute period costs 10 cents.

For example, in a 10-minute call:

• Subtract the first 3 minutes: 10 - 3 = 7 minutes.
• Divide 7 by 3: 7 / 3 = 2 full periods + partial period.
• Count the 2 full and 1 partial period: 2 + 1 = 3 periods in total at 10 cents each.

This makes a total of 30 cents for the additional periods, plus the initial 25 cents, resulting in 55 cents total.

problem-solving steps

Approaching problems systematically helps in understanding and finding a solution efficiently. Here's how you can solve these types of payment calculations:

• Step 1: Understand the charge rule. Clearly define how the charges are applied over time.
• Step 2: Break down the time. Separate the initial period where a different rate might apply, then divide the remaining time by the given units.
• Step 3: Apply the charges. Calculate the cost for each period and add them together to get the total.

Consider the given exercise:

• For part (a): After understanding the rule, break down the 10 minutes into the initial 3 minutes and the remaining 7 minutes. Calculate the cost for the initial and remaining time and sum them up.
• For part (b): Convert the total money available into cents. After subtracting the initial charge, divide the remaining money by the cost per segment to determine how many full segments you can afford. Multiply this by the time unit to find out the talk time.

By following these steps, you can ensure a precise and methodical solution.