Question

Team Aand Team Btake part in a quiz league.
After 11 rounds, Team Ahas a mean score per round of 17
After 9 rounds, Team Bhas a mean score per round of 18
Both teams take part in a further round.
After this round, both teams have a mean score per round of 18.5
In the further round, Team Ascored more points than Team B.
How many more?

Answer 1

Let's break down the information given:

- After 11 rounds, Team A has a mean score per round of 17.
- After 9 rounds, Team B has a mean score per round of 18.
- After a further round, both teams have a mean score per round of 18.5.
- In this further round, Team A scored more points than Team B.

To solve this, we'll first find the total points each team had before the further round.

For Team A:
Total points before the further round = Mean score per round * Number of rounds
= 17 * 11
= 187

For Team B:
Total points before the further round = Mean score per round * Number of rounds
= 18 * 9
= 162

Now, let's denote x as the number of points Team A scored in the further round. Since both teams have a mean score per round of 18.5 after the further round, we can set up the equation:

(Total points of Team A + x) / (Number of rounds for Team A + 1) = 18.5

Plugging in the values:
(187 + x) / 12 = 18.5

Now, we can solve for x:
187 + x = 18.5 * 12
187 + x = 222
x = 222 - 187
x = 35

So, Team A scored 35 points in the further round.

Now, we need to find out how many more points Team A scored than Team B in this further round:
Points scored by Team A - Points scored by Team B = 35 - 18 = 17

Therefore, Team A scored 17 more points than Team B in the further round.