Problem 42 - Algebra 2

Question

Masao has a long-distance telephone plan where she pays 10\(\notin\) for each minute or part of a minute that she talks, regardless of the time of day. How much would a call that lasts 9 minutes and 40 seconds cost?

Step-by-Step Solution

Answer

The call costs 1 euro.

Step 1: Convert Time to Minutes

First, convert the call duration into total minutes. The call lasted 9 minutes and 40 seconds. Since 40 seconds is less than a full minute, we need to round up to the nearest minute because Masao is charged per whole minute. So, 9 minutes and 40 seconds rounds up to 10 minutes.

Step 2: Calculate Cost of Call

Now that we have determined that the call lasted for 10 minutes, we can calculate the total cost. Masao pays 10 cents per minute. Therefore, the total cost is \(10\) minutes \(\times\) 10 cents/minute = 100 cents.

Step 3: Convert Cents to Euros

Finally, convert the cost from cents to euros. Since 100 cents make up 1 euro, the cost of the call is 1 euro.

Key Concepts

Unit Conversion

Unit conversion is an essential math skill, especially when you need to solve problems involving different measurements. When converting units, you’re essentially translating one kind of measurement into another. For instance, in the context of the phone call scenario, we're dealing with time. The call duration is given in minutes and seconds, where seconds need to be integrated into minutes.
To convert seconds to minutes, recall that 60 seconds make up one minute. If you have 40 seconds, you divide by 60 to express it in minutes:

• \[ \text{40 seconds} = \frac{40}{60} \text{ minutes} \approx 0.67 \text{ minutes} \]

Adjustments are often made in real-world scenarios where charges are applied. Here, each part of a minute counts as a full minute when calculating charges. This conversion ensures the phone call duration of 9 minutes and 40 seconds is noted as 10 full minutes, as businesses might not charge partial usage of a service.

Step-by-Step Problem Solving

Step-by-step problem solving is a strategy you can use to break down complex problems into manageable steps. Each step focuses on solving part of the problem, leading to the solution. In our telephone call cost problem, the step-by-step approach simplifies the calculation:

• First, convert any time measurements to a common unit, so you understand the total duration. Here, the call lasts for 9 minutes and 40 seconds, converting this into 10 minutes for charge purposes.
• Second, apply the cost per unit. Masao is charged 10 cents for every minute, so multiply the number of minutes (10) by the rate (10 cents per minute) to find the total cost.
• Lastly, transform the calculated charge from smaller currency units (cents) to larger units (euros), as requested. Since 100 cents equal 1 euro, a cost of 100 cents converts exactly to 1 euro.

Utilizing each of these steps ensures a comprehensive approach, making sure all details are covered for precise and clear solutions.

Rounding Numbers

Rounding numbers is crucial when exact precision is not necessary or when simplifying numbers for practical applications, like billing. In Masao's case, the rounding method is dictated by the billing rules: any part of a minute needs to be rounded up to the next full minute, no matter how small. This approach is typical in billing systems to cover partial usage:

• Masao talks for 9 minutes and 40 seconds. Since 40 seconds is not fully a minute but greater than zero, it rounds up.
• Thus, the total rounded time is 10 minutes, resulting in Masao being charged for 10 full minutes.

Remember, rounding generally follows this rule: if the remaining seconds or smaller unit is more than halfway, round up. This process ensures fair billing practice from the provider's perspective and is crucial in real-world scenarios where estimates derive final costs.