Chapter 15.3, Problem 21P

* Ms. Smith needs to figure her students’ homework grades. There have been 5 homework assignments: the first with 30 points, the second with 40 points, the third with 30 points, the fourth with 50 points, and the fifth with 25 points. Ms. Smith is debating between two different methods of calculating the homework grades.
Method 1: Add up the points scored on all 5 of the homework assignments, and divide by the total number of points possible. Then multiply by 100 to get the total score out of 100.
Method 2: Find the percentage correct on each homework assignment, and find the average of these five percentages.
a. Jodi’s homework grades are $\frac{27}{30},\frac{25}{40},\frac{26}{30},\frac{30}{50},\frac{24}{25}$ , where, for example, $\frac{27}{30}$ stands for 27 points out of 30 possible points in a homework assignment. Compare how Jodi does with each of the two methods. Which method gives her a higher score?
b. Make up scores (on the same assignments) for Robert so that Robert scores higher with the other method than the one that gave Jodi the higher score.