Second Half Score
Boarwarts Academy played their annual match against Range Hill School. What fraction of the points were scored in the second half?
Age
11 to 14
Challenge level
Problem
In the first half of their match against Range Hill School, Boarwarts Academy scored all of the points.
In the second half, each side scored three points.
At the end of the match, Boarwarts Academy had scored $90\%$ of the points.
What fraction of the points were scored in the second half?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: $\frac15$
Using percentages
Range Hill
First half: 0 points
Second half: 3 points
Total 10%
Boarwarts
Second half: 3 points, which is also equal to 10%
$\therefore$ total of 10% + 10% = 20% of points were scored in the second half
20% = $\frac15$
Finding the total number of points
Range Hill
First half: 0 points
Second half: 3 points
10% = 3 points
100% = 30 points
Boarwarts 3 points in second half $\therefore$ total 6 points in second half
$\frac6{30}=\frac15$