Question

Multiple Choice Charo walks 15 minutes the first day, 22 minutes the second day, and 29 minutes the third day. If she continues this pattern, how many minutes will Charo walk the fifth day? (Lesson 1-1) (A) \(33 \mathrm{~min}\) (B) \(36 \mathrm{~min}\) (C) \(39 \mathrm{~min}\) (D) \(43 \mathrm{~min}\)

Short answer

43 minutes (Option D).

Step-by-step solution

Identify the pattern

Observe the time Charo walks each day: 15 minutes, 22 minutes, and 29 minutes. Notice that each day, Charo increases the amount of walking by a constant number of minutes.

Determine the change between days

Calculate the difference in minutes between consecutive days: \(22 - 15 = 7\) minutes and \(29 - 22 = 7\) minutes. Charo's walking time increases by 7 minutes each day.

Continue the pattern

To find the walking time for the fourth and fifth day, continue adding 7 minutes for each subsequent day. For the fourth day, add 7 minutes to the third day: \(29 + 7 = 36\) minutes.

Calculate the fifth day's walking time

Add 7 minutes to the time of the fourth day: \(36 + 7 = 43\) minutes. Therefore, based on the pattern, Charo will walk 43 minutes on the fifth day.

Key concepts

Pattern Recognition

Recognizing patterns is an essential skill in mathematics, especially when dealing with sequences. In the given exercise, Charo's walking times follow a specific pattern. To identify this pattern, observe the differences between consecutive terms. The sequence starts with 15 minutes, then 22 minutes, and 29 minutes.

• Notice the increase from one day to the next. Each subsequent day, the walking time increases by 7 minutes.
• This constant difference is the key to recognizing that we are dealing with an arithmetic sequence.

By identifying the constant difference, we are equipped to predict future terms without difficulty. This method of prediction makes it straightforward to calculate future walking durations for Charo.

Problem Solving

Problem-solving involves the strategic process used to derive the correct solution to a given problem. In the context of this arithmetic sequence, the key challenge is to predict the number of minutes Charo will walk on subsequent days based on the established pattern.

• First, acknowledge the established pattern, which is increasing by 7 minutes daily.
• Then, calculate the time for the fourth day by adding 7 to the third day’s walk time: 29 + 7 = 36 minutes.
• Finally, add 7 minutes to the fourth day to find the fifth day's time: 36 + 7 = 43 minutes.

By following this systematic approach, you can solve similar problems with confidence and accuracy, ensuring that each step logically follows the next.

Mathematical Reasoning

Mathematical reasoning is the logical thought process that leads to conclusions based on facts, relationships, and principles. When handling arithmetic sequences, reasoning through the sequence involves confirming that a constant increment or decrement applies.

• Start by understanding that arithmetic sequences increase or decrease by a set interval, known as the common difference.
• Apply this understanding to assess whether each step in the sequence follows the established rule—adding 7 in this example.
• Predict the continuation of the sequence by applying the same rule; add 7 minutes day-by-day to project the walking times.

Mathematical reasoning transforms pattern recognition and problem-solving into structured, logical methods. It allows you to anticipate outcomes based on principles, either verifying the established pattern or correcting it when anomalies arise.