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In warmer climates, approximate temperature predictions can be made by counting the number of chirps of a cricket during a minute. The Fahrenheit temperature
decreased by forty is equivalent to one-third of the number of cricket chirps.
(a) Write an equation for this relationship.
(b) Approximately how many chirps per minute should be recorded if the temperature is 90°F?
(c) If a person recorded 72 cricket chirps in a minute, what would be the Fahrenheit temperature according to this formula?
(a) Let F represent the Fahreheit temperature and let x represent the number of chirps. The equation for this relationship is
(Use integers or fractions for any numbers in the expression.)

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The relationship between temperature and the number of chirps based on the information given goes thus :

  • 150 chips
  • 64°F
  • [tex] f - 40 = \frac{x}{3}[/tex]

Let :

  • Temperature = f ; number of cricket chirps = n
  • [tex] f - 40 = \frac{n}{3}[/tex]

1.) Chirps per minute if temperature is 90°F

Put f = 40°F into the equation :

[tex] 90 - 40 = \frac{n}{3}[/tex]

[tex] 50 = \frac{n}{3}[/tex]

[tex] n = 50 \times 3 = 150 chirps [/tex]

2.) Fahrenheit temperature if n = 72

[tex] f - 40 = \frac{72}{3}[/tex]

Cross multiply

[tex] 3(f - 40) = 72[/tex]

[tex] 3f - 120 = 72[/tex]

[tex] 3f = 72 + 120 [/tex]

[tex] 3f = 192[/tex]

[tex] f = \frac{192}{3} = 64 [/tex]

3.)

The equation for the relationship with f = Fahrenheit temperature and x = number of chirps

[tex] f - 40 = \frac{x}{3}[/tex]

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