.:Problem One:.

Part A: The Swimming Races

Three girls, Sarah, Michelle And Catherine, held a series of swimming races among themselves.

- They decided to award a positive whole number of points for finishing first, second and third.
- The number of points for first was more than the number of points for second which was more than the number for third.
- The same number of points was awarded for the same place in each race.
- There were no ties.

The first race was breaststroke.

Altogether Sarah accumulated 20 points, Michelle 10 points and Catherine 9 points.

a. How many races were there and how many points were awarded for each race?

b. How many points were awarded for first, second and third in each race? Explain.

c. If Sarah did not win the backstroke race, who did win the backstroke?

Part B: The examination.

An examination question is marked out of 5 and only whole marks are given.

Five people answer the question.

The mode of their marks is one more than the median which is one more than the mean.

What marks did each person get? Explain.