indhu played ten games in the badminton tournament. Her scores in the sixth, seventh, eighth, and ninth games were 22, 16, 14, and 20 points respectively. Her points-per-game average was higher after nine games than it was after the first five games. If her average after ten games was greater than 19, what is the minimum number of points she could have scored in the tenth game?1)  312)  303)  294)  28

To solve this problem, we first need to understand that the average score is the total points scored divided by the number of games played.

1. We know that Indhu's average after nine games was higher than her average after five games. This means that the total points she scored in games 6, 7, 8, and 9 (22 + 16 + 14 + 20 = 72 points) was higher than five times her average after five games.

2. We also know that her average after ten games was greater than 19. This means that the total points she scored in all ten games was greater than 190 (10 games * 19 points/game).

3. To find the minimum number of points she could have scored in the tenth game, we need to subtract the total points she scored in the first nine games from 190.

4. Since we don't know the exact number of points she scored in the first five games, we can assume that she scored the minimum possible, which is 72 points (the total points she scored in games 6, 7, 8, and 9).

5. So, the minimum number of points she could have scored in the tenth game is 190 - 72 = 118 points.

However, this number seems too high for a badminton game. It's possible that there's a mistake in the problem or that I misunderstood it. Could you please check the problem again?

To solve this problem, we first need to calculate the total points Indhu scored in the first nine games. We know that she scored 22, 16, 14, and 20 points in the sixth, seventh, eighth, and ninth games respectively. However, we don't know the exact scores for the first five games. We only know that her average score after nine games was higher than it was after the first five games.

Let's assume that her average score after the first five games was A. This means that the total score for the first five games was 5A.

After nine games, her average score was higher than A. Let's assume it was A + B. This means that the total score for the first nine games was 9(A + B).

We can set up the equation 5A + 22 + 16 + 14 + 20 = 9(A + B). Simplifying this gives us 5A + 72 = 9A + 9B.

We can rearrange this to find that 4A = 72 - 9B. Since A must be a positive number (she must have scored some points in the first five games), this means that B must be less than 8.

Now, we know that her average score after ten games was greater than 19. This means that the total score after ten games was greater than 190.

If we assume that she scored the minimum number of points in the tenth game, we can set up the equation 9(A + B) + X > 190, where X is the score in the tenth game.

Substituting 4A = 72 - 9B into this equation gives us 72 + X > 190. Solving for X gives us X > 118.

Therefore, the minimum number of points she could have scored in the tenth game is 119. However, this is not one of the options given. This suggests that there may be a mistake in the problem or in our calculations.

To solve this problem, we first need to understand that the average score is the total points scored divided by the number of games played.

Given that Indhu's average after nine games was higher than it was after the first five games, we can infer that the total points she scored in the sixth, seventh, eighth, and ninth games is higher than five times her average after five games.

The scores for the sixth, seventh, eighth, and ninth games are given as 22, 16, 14, and 20 respectively. Adding these up gives us a total of 72 points.

So, five times her average after five games is less than 72.

Now, we know that her average after ten games was greater than 19. This means that the total points she scored in ten games is more than 190 (because 19*10 = 190).

Since we already know she scored 72 points in the sixth to ninth games, the minimum number of points she could have scored in the first five games and the tenth game combined is 190 - 72 = 118.

However, since her average after five games is less than the average after nine games, she must have scored less than 72 points in the first five games. Let's assume she scored 71 points in the first five games.

This would mean that the minimum number of points she could have scored in the tenth game is 118 - 71 = 47.

However, the options provided in the question do not include 47. This suggests that there may be a mistake in the question or in our calculations.

Let's try a different approach.

If we assume that she scored the same number of points in the first five games as she did in the sixth to ninth games (72 points), her total after nine games would be 144 points.

To have an average of more than 19 after ten games, she would need to score at least 196 points in total.

This means that the minimum number of points she could have scored in the tenth game is 196 - 144 = 52.

Again, this is not one of the options provided in the question.

Therefore, based on the information provided in the question, it is not possible to determine the minimum number of points Indhu could have scored in the tenth game.