Problem 32 - Prealgebra

Question

Use the following information. The number of times a cricket chirps can be used to estimate the temperature in degrees Fahrenheit. Use \(c \div 4+37,\) where \(c\) is the number of chirps in 1 minute. What is the temperature if a cricket chirps 100 times in a minute?

Step-by-Step Solution

Answer

The temperature is 62 degrees Fahrenheit.

Step 1: Understand the Formula

The formula provided is \( T = \frac{c}{4} + 37 \), where \( T \) is the temperature in degrees Fahrenheit and \( c \) is the number of chirps in one minute. This formula tells us that we first divide the chirps by 4, then add 37 to find the temperature.

Step 2: Substitute Chirps in Formula

Substitute the given number of chirps, \( c = 100 \), into the formula: \( T = \frac{100}{4} + 37 \).

Step 3: Divide Chirps by 4

Calculate \( \frac{100}{4} \). This equals 25. So, the formula becomes \( T = 25 + 37 \).

Step 4: Add 37 to the Result

Add 37 to the result from the previous step: \( 25 + 37 = 62 \).

Step 5: Conclusion

The calculated temperature is 62 degrees Fahrenheit. Therefore, if a cricket chirps 100 times in a minute, the estimated temperature is 62 degrees Fahrenheit.

Key Concepts

Problem Solving

Problem solving is a key skill in mathematics. It involves understanding the problem, identifying the formula or concept needed, and applying the right operations to find a solution. In this exercise, the goal is to estimate the temperature based on the cricket's chirp rate. To solve the problem, we start with knowing how many times a cricket chirps—in this case, 100 times per minute. We then identify the given formula: \[ T = \frac{c}{4} + 37 \]This formula is used to convert cricket chirps into an estimate of temperature in degrees Fahrenheit.Steps to Apply Problem Solving:

• Identify the Information: Start by defining what is given (chirps) and what you need to find (temperature).
• Use the Correct Formula: Here, the formula involves dividing chirps by 4 and adding 37.
• Step-by-step Approach: Break down calculations into smaller steps—divide, then add.

This systematic problem-solving approach helps in arriving at the correct answer efficiently.

Temperature Estimation

Temperature estimation using cricket chirps is a fascinating concept. Crickets are cold-blooded creatures, and their chirping rate varies with temperature. This biological behavior can be quantified using an algebraic formula.Understanding Temperature Estimation:

• Chirp Rate: The chirp rate increases as temperature rises. By counting these chirps, we can estimate how warm it is.
• Formula Application: The formula \( T = \frac{c}{4} + 37 \) simplifies the process of estimating temperature based on observed chirps.
• Practical Use: This practical method offers an intuitive way for entomologists and nature enthusiasts to estimate ambient temperature.

The simplicity of involving only addition and division makes it accessible for anyone curious about their surroundings.

Mathematical Operations

Mathematical operations are at the core of solving algebraic formulas. In our cricket-chirping problem, we employ two basic operations: division and addition. Breaking Down Mathematical Operations:

• Division: When we divide the number of chirps by 4, we're essentially scaling down the rate to plug into our formula. For chirps of 100 times per minute, dividing by 4 gives us 25.
• Addition: Adding 37 to our result from division adjusts the scaled value to provide a real-world temperature estimate. Hence, adding 37 to 25 gives us 62 degrees Fahrenheit.
• Accurate Calculation: Performing these operations accurately results in the correct estimation of the temperature based on biological data.

Understanding and mastering these mathematical operations aids greatly in problem solving, not just in this exercise, but in a wide array of real-world applications.