The swimming pool is open when the high temperature is higher than 20^(@)C. Lainey tried to swim on Monday and Thursday (which n is 3 days later). The pool was open on Monday, but it was closed on Thursday. The high temperature was 30C on Monday. but decreased at a constant rate in the next 3 days. Write an inequality to determine the rate of temperature decrease in degrees Celsius per day, d, from Monday to Thursdí/. What is the solution set of the inequality?

Question

The swimming pool is open when the high temperature is higher than  20^(@)C. Lainey tried to swim on Monday and Thursday (which  n is 3 days later). The pool was open on Monday, but it was closed on Thursday. The high temperature was  30C on Monday. but decreased at a constant rate in the next 3 days. Write an inequality to determine the rate of temperature decrease in degrees Celsius per day,  d, from Monday to Thursdí/. What is the solution set of the inequality?

Bytelearn · Accepted Answer

Write Inequality: Let's denote the rate of temperature decrease in degrees Celsius per day as $ d $. Since the temperature was $ 30^\circ C $ on Monday and the pool is closed when the temperature is $ 20^\circ C $ or lower, we can write an inequality to represent the temperature on Thursday. The temperature on Thursday would be the temperature on Monday minus the rate of decrease times the number of days, which is 3 days in this case. So, the inequality is: $ 30 - 3d > 20 $Isolate Term: Now, we need to solve for $ d $. To do this, we will subtract $ 30 $ from both sides of the inequality to isolate the term with $ d $. $ 30 - 3d - 30 > 20 - 30 $ This simplifies to: $ -3d > -10 $Divide and Reverse: Next, we divide both sides of the inequality by $ -3 $ to solve for $ d $. Remember that when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign. $ \frac{-3d}{-3} < \frac{-10}{-3} $ This simplifies to: $ d < \frac{10}{3} $Solution Set: The solution set for the inequality is all values of $ d $ that are less than $ \frac{10}{3} $ degrees Celsius per day. This means that the rate of temperature decrease per day must be less than $ \frac{10}{3} $ degrees Celsius for the pool to have been open on Monday and closed by Thursday.

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