George wants to run a mile race in under minutes. Halfway through the race, at mile George’s personal trainer, Haile, gives him a note that reads What is Haile trying to tell George? Interpret and solve the inequality.
To begin, we can interpret each side of the inequality separately. Let's begin with the right-hand side since it only has one term. We know that George wants to finish the race in less than minutes. Thus, the right-hand side of the inequality represents George's maximum time. The left-hand side, is more complicated. We can think of George's total time in terms of the time it takes to run the first half and the second half separately. When Haile passes George the note, the first half of the race is completed. Thus, represents the number of minutes it took George to run the first half of the race. The term represents the time George can take to run the second half of the race while still meeting his goal. Since is the number of miles left to run, must be the maximum time per mile George can take.
Bear cubs are born during winter and first come out of their den in spring. Suppose spring begins once the mean temperature during a five day period is higher than Following a period of cold weather, four warmer days were registered in the forest. The highest temperatures these days were and How warm must the fifth day be for the cubs to come out of their den?
Here, highlight the important information from the situation.
Typically, a variable is used to represent an unknown quantity in a situation. Here, the unknown quantity is the highest temperature on the fifth day. The variable can be used to represent the highest temperature that day.
Next, it is necessary to understand how the different quantities in the problem relate. The mean temperature over five days is the sum of the highest temperatures each day, divided by the number of days, Since the mean must be greater than the following inequality can be written.
Creating the inequality involves translating the relationship from Step into symbols. The mean of a data set can be calculated using Thus, the mean temperature over five days can be found by adding the given temperatures and dividing by the the number of temperatures. Replace the right-hand side of this expression into the inequaltiy from Step 3.