Maths-
SAT
Easy

Question

g left parenthesis t right parenthesis equals fraction numerator 5 left parenthesis 7 t minus 12 c right parenthesis over denominator 2 end fraction minus 25
The number of people who go to a public swimming pool can be modeled by the  function g above, where c is a constant and t is the air temperature in degrees   Fahrenheit (°F) for 70 < t < 100. If 350 people are predicted to go to the pool when  the temperature is 90°F, what is the value of c ?

  1. 20
  2. 40
  3. 60
  4. 80

The correct answer is: 40


    Given g left parenthesis t right parenthesis equals fraction numerator 5 left parenthesis 7 t minus 12 c right parenthesis over denominator 2 end fraction minus 25
    Temperature t = 90˚.
    350 equals fraction numerator 5 left parenthesis 7 left parenthesis 90 right parenthesis minus 12 c right parenthesis over denominator 2 end fraction minus 25
    350 + 25 equals fraction numerator 5 left parenthesis 630 minus 12 c right parenthesis over denominator 2 end fraction
    375 × 2 = 5(630 – 12c)
    750 over 5 equals 630 minus 12 c
    150 = 630 – 12c
    12c = 630 – 150
    12c = 480
    c equals 480 over 12
    c = 40.

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