SOLUTION: Biologists have found that the number of chirps some crickets make per minute is related to temperature. When crickets chirp 124 times a minute, it is about 68 degrees Fahrenheit.

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Question 1184603: Biologists have found that the number of chirps some crickets make per minute is related to temperature. When crickets chirp 124 times a minute, it is about 68 degrees Fahrenheit. When they chirp 172 times a minute, it is about 80 degrees Fahrenheit. How warm is it when the crickets are chirping 150 times a minute?
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
x = chirps, y = degrees

>>>When crickets chirp 124 times a minute, it is about 68 degrees Fahrenheit. 

So when x = 124, y = 68.  So the graph of the equation contains the point
(124,68)

>>>When they chirp 172 times a minute, it is about 80 degrees Fahrenheit.

So when x = 172, y = 80.  So the graph of the equation contains the point
(172,80)

We assume the graph of the equation is a straight line.

So we use the slope formula to find the slope of the line

m%22%22=%22%22%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

m%22%22=%22%22%28%2880%29-%2868%29%29%2F%28%28172%29-%28124%29%29

m%22%22=%22%22%2812%29%2F%2848%29%22%22=%22%221%2F4

We use the point-slope equation:

y-y%5B1%5D%22%22=%22%22m%28x-x%5B1%5D%29

y-%2868%29%22%22=%22%22expr%281%2F4%29%28x-%28124%29%5E%22%22%29

y-68%22%22=%22%22expr%281%2F4%29x-expr%281%2F4%29%28124%29

y-68%22%22=%22%22expr%281%2F4%29x-31

Add 68 to both sides

y%22%22=%22%22expr%281%2F4%29x%2B37

>>>How warm is it when the crickets are chirping 150 times a minute?

Substitute x = 150:

y%22%22=%22%22expr%281%2F4%29%28150%29%2B37

y%22%22=%22%2237.5%2B37

y%22%22=%22%2274.5degreesFahrenheit

Edwin

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


A formal algebraic solution like the one provided by the other tutor is probably what was expected from the student.

But the same calculations can be done informally to reach the answer faster and with less work.

The two given temperatures are 68 and 80 degrees, a difference of 12 degrees.
The two rates of chirping are 124 and 172, a difference of 48.

Assuming a linear relationship (which should be stated in the problem, but which we have to assume in order to solve the problem), the rate of chirping increases by 48/12=4 for each increase of 1 degree of temperature.

150 chirps per minute is 26 more than the 124 per minute at 68 degrees. Since the rate of increase is 4 chirps for each degree increase of temperature, the increase in temperature from 68 degrees to get 150 chirps per minute is 26/4=6.5 degrees. So

ANSWER: The temperature at which the crickets will chirp at a rate of 150 per minute is 68+6.5=74.5 degrees.

All the words of explanation make this sound like a long and complicated problem. But the calculations alone are few and easy:

80-68=12
172-124=48
48/12=4
150-124=26
26/4=6.5
68+6.5=74.5