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December 21, 2014

December 21, 2014

Posted by **Gina** on Saturday, October 7, 2006 at 1:00pm.

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.

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