The Snowtree cricket behaves in a rather interesting way: The rate at which it chirps depends linearly on the temperature. One summer evening you hear a cricket chirping at a rate of 140 chirps per minute, and you notice that the temperature is 80°F. Later in the evening, the cricket has slowed down to 120 chirps per minute, and you notice that the temperature has dropped to 75°F. What is the temperature if the cricket is chirping at a rate of 108 chirps per minute ?
A)72°F
B) 70°F
C) 78°F
D) 67°F
E) 76°F

Question

The Snowtree cricket behaves in a rather interesting way: The rate at which it chirps depends linearly on the temperature. One summer evening you hear a cricket chirping at a rate of 140 chirps per minute, and you notice that the temperature is 80°F. Later in the evening, the cricket has slowed down to 120 chirps per minute, and you notice that the temperature has dropped to 75°F. What is the temperature if the cricket is chirping at a rate of 108 chirps per minute  ?
A)72°F
B) 70°F
C) 78°F
D) 67°F
E) 76°F

Quizplus · Accepted Answer

To find the relationship between chirps per minute and temperature, we can use the two given points: (140, 80) and (120, 75). The slope (m) of the line representing this relationship is (80-75) / (140-120) = 5/20 = 1/4. This means the temperature increases by 1°F for every 4 chirps per minute increase. Using one of the points to find the equation of the line, y = mx + b, we get 80 = (1/4)*140 + b, solving for b gives b = 45. The equation relating temperature (T) to chirps per minute (C) is T = (1/4)C + 45. Substituting 108 chirps per minute into this equation gives T = (1/4)*108 + 45 = 27 + 45 = 72°F.

The Snowtree Cricket Behaves in a Rather Interesting Way: the Rate