Question

1. you can determine the approximate temperature in degrees fahrenheit by counting the number of times a cricket chirps in one minute. then multiply that by 7, divide by 30, and add 40. see example 4 1x7÷30 + 40

a. write a formula for estimating the temperature based on the number of cricket chirps.
b. write a new formula for the number of chirps you would expect in one minute at a given fahrenheit temperature.
c. use the formula to find the number of chirps in one minute when the temperature is 89°f.

Explanation:

Step1: Define variables

Let $C$ be the number of cricket - chirps per minute and $T$ be the temperature in degrees Fahrenheit.

Step2: Write the temperature - chirp formula

Based on the problem description, the formula for estimating the temperature is $T=\frac{7C}{30}+40$.

Step3: Solve for $C$ in terms of $T$

Starting with $T = \frac{7C}{30}+40$, first subtract 40 from both sides: $T - 40=\frac{7C}{30}$. Then multiply both sides by $\frac{30}{7}$ to get $C=\frac{30(T - 40)}{7}$.

Step4: Find the number of chirps when $T = 89$

Substitute $T = 89$ into the formula $C=\frac{30(T - 40)}{7}$. First, calculate $T-40$: $89 - 40=49$. Then, $C=\frac{30\times49}{7}$. Since $\frac{49}{7}=7$, then $C = 30\times7=210$.

Answer:

a. $T=\frac{7C}{30}+40$
b. $C=\frac{30(T - 40)}{7}$
c. 210