Chapter 1.5, Problem 44PPSE

Solution

The maximum time she can score on her last trial to get an average time of all four trials under 36 seconds.

  $36.61$ seconds

Given:

A scores of the first three trials of a skater are 35.52 seconds, 36.04 seconds, and 35.82 seconds.

Concept Used:

• If there is the strict inequality symbol $<\text{ or}>$, then use a parenthesis $\left(\right)$ on the interval
• If there is the inequality symbol $\le \text{ or}\ge$, then use a bracket $\left[\right]$ on the interval
• To graph the endpoint with strict inequality $<\text{ or}>$, use the open parenthesis or a hollow circle at that endpoint.
• To graph the endpoint with inequality symbol $\le \text{ or}\ge$, use the bracket or a solid circle at that endpoint.
• Multiplying or dividing an inequality by a negative number reverse the inequality sign.
• Average is the quotient of the sum of all data points and the number of data points.

Calculation:

Let x be the number of seconds that she can score on her last trial.

Since the average of all four trials should be under 36 seconds, it follows

  $\begin{array}{c}\text{Average of 4 trials}<36\text{ seconds}\\ \frac{\text{Sum of all 4 trials}}{4}<36\\ \frac{35.52+36.04+35.82+x}{4}<36\\ \frac{107.38+x}{4}<36\\ \frac{107.38+x}{4}\cdot 4<36\cdot 4\\ 107.38+x<144\\ x<144-107.38\\ x<36.62\end{array}$

Thus, the maximum time she can score on her last trial is $36.61$ seconds.