Question

A public beach assigns work shifts to its lifeguards based on the estimated daily attendance. For each 1°F increase in temperature, an estimated 45 additional people come to the beach. On Saturday it reached a temperature of 88°F and beach attendance was 1050. On Sunday it is forecast to be only 77°F. What is the projected attendance for Sunday?

Answer 1

Answer: 555

Explanation:

Let x represents the temperature in Fahrenheit and y represents the number of people come.

Here, the rate of increasing the number of people is constant (45) for every degree of Fahrenheit.

Thus, the equation that represents the given situation is,

y = 45 x + c ------(1)

Where c is any constant.

According to the question,

For, x = 88°, y = 1050

Then, from equation (1),

1050 = 45 × 88 + c

⇒ c = 1050 - 45 × 88 = -2910

Thus, the final equation that shows the given situation,

y = 45 x - 2910

For, x = 77,

y = 45 × 77 - 2910 = 3465 - 2910 = 555

The projected attendance for Sunday is 555 people.