Photo AI
The table shows the relative frequencies of the results for a football team after a number of games - OCR - GCSE Maths - Question 5 - 2018 - Paper 1
Question 5
The table shows the relative frequencies of the results for a football team after a number of games. | Result of game | won | lost | drew | |----------------|-----|... show full transcript
Worked Solution & Example Answer:The table shows the relative frequencies of the results for a football team after a number of games - OCR - GCSE Maths - Question 5 - 2018 - Paper 1
Step 1
Complete the table.
Answer
To complete the table, we need to determine the relative frequency of the 'drew' category. We know that the sum of all relative frequencies must equal 1.
Calculating the missing relative frequency for 'drew':
Thus, the completed table is:
| Result of game | won | lost | drew |
|---|---|---|---|
| Relative frequency | 0.2 | 0.45 | 0.35 |
Step 2
The team lost 10 more games than they won.
Answer
Let the number of games won be denoted as 'W'. According to the problem, the number of games lost 'L' can be expressed as:
Next, we will use the relative frequencies to find the total number of games played, denoted as 'T'. We can express the number of games won as:
From the rewritten expression for L:
Now, substituting the expression for 'W' into the equation for 'L':
To solve for T, we rearrange the equation:
This simplifies to:
Finally, solving for T gives:
T = rac{10}{0.25} = 40
Thus, the team played a total of 40 games.