This seems like an easy question yet I am not able to comprhend.
Question: Inher latest game, Mary bowled 199 and raised her average to 179 from 178. To raise her average to 180 with the next game, what must she bowl?
Her average was 178. The average is the sum of the scores divided by the games played, so 178 = scores/#games, or #games*178=scores. Now add the new score to get
(#games+1)*179=scores + 199
If you substitute the previous score=#games*178 into the second equation to get
(#games+1)*179=#games*178 + 199 or
#games=20
So you now know the original number of games bowled to get 178 for the average was 20 and the scores added to 20*178=3560
She then bowled 199 in the 21st game so (3560+199)/21 = 179
So now she wants to bowl 22 games and get an average of 180, so the score need to add to 22*180=3960
So subtract the scores from the 21 games rolled to see what she needs to roll on the 22nd game to raise the average 1 point.
There's probably a simple proportion way to solve this too, but the way I solved it verifes everyting you can know about the scores.
To answer the question, we start by understanding Mary's current average of 179. We know that her average is the sum of the scores divided by the number of games played. So, we have the equation:
(#games + 1) * 179 = scores + 199
To find the number of games, we substitute the previous score (which was #games * 178) into the equation:
(#games + 1) * 179 = #games * 178 + 199
We solve this equation to find that the original number of games bowled to get an average of 178 was 20, and the sum of the scores was 20 * 178 = 3560.
Next, we factor in the score of the 21st game, which was 199, to find Mary's average of 179. We have the equation:
(3560 + 199) / 21 = 179
To raise her average to 180, Mary needs to bowl 22 games with a total score of 22 * 180 = 3960.
To find out what she needs to bowl on the 22nd game to raise her average by 1 point, we subtract the sum of the scores from the first 21 games (3560) from the desired total score of 3960. The difference is the score she needs to bowl in the 22nd game.