Question

Ratios

Last season, a rugby team won half of their matches by more than 10 points and a quarter of their matches by less than 10 points. They lost the rest. Find the team's ratio of wins to losses

Answer 1

Let's say the team played a total of x matches. Then:

- They won half of their matches by more than 10 points, so they won 1/2 x/2 = x/4 matches by more than 10 points.
- They won a quarter of their matches by less than 10 points, so they won 1/4 x/4 = x/16 matches by less than 10 points.
- They lost the rest, which is x - x/4 - x/16 = 9x/16 matches.

So the team won a total of x/4 + x/16 = 5x/16 matches. Therefore, the ratio of wins to losses is:

wins : losses = 5x/16 : 9x/16 = 5:9

Answer: 5:9