The table shows the relative frequencies of the results for a football team after a number of games - OCR - GCSE Maths - Question 18 - 2018 - Paper 1

Let the number of games won be denoted as $x$. Since the team lost 10 more games than they won, the number of games lost will be $x + 10$.

Using the relative frequencies:

• The overall relative frequency of lost games is 0.45, which means:

rac{x + 10}{N} = 0.45

where $N$ is the total number of games played.

From part (a), we also have:

rac{x}{N} = 0.2 ext{ (for won games)}

Now substituting $x = 0.2N$ into the lost games equation:

rac{0.2N + 10}{N} = 0.45

Simplifying the equation:

$$0.2N + 10 = 0.45N$$ $$10 = 0.45N - 0.2N$$ $$10 = 0.25N$$

So,

N = rac{10}{0.25} = 40

The team played a total of 40 games.