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
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
To find the team's ratio of wins to losses, we need to determine the number of wins and losses separately.
Let's assume the team played a total of "x" matches in the last season.
According to the information given, the team won half of their matches by more than 10 points. This means they won (1/2) * x matches by more than 10 points.
The team also won a quarter of their matches by less than 10 points. So, they won (1/4) * x matches by less than 10 points.
To calculate the number of matches they lost, we subtract the total number of matches they won from the total matches played:
Number of Matches Lost = Total Matches - (Matches Won by >10 points + Matches Won by <10 points)
Number of Matches Lost = x - [(1/2) * x + (1/4) * x]
= x - (1/2 + 1/4) * x
= x - (3/4) * x
= (1/4) * x
Therefore, the team lost (1/4) * x matches.
Now, let's calculate the ratio of wins to losses:
Ratio of Wins to Losses = Matches Won / Matches Lost
= [(1/2) * x + (1/4) * x] / (1/4) * x
= [(2/4) * x + (1/4) * x] / (1/4) * x
= (3/4) * x / (1/4) * x
= (3/4) / (1/4)
= 3/1
= 3
Therefore, the team's ratio of wins to losses is 3:1.