math
posted by sara .
Jane and Kathy are playing a game of marbles. In each game the loser gives the other girl a marble. When they are finished Jane had won 15 times and Kathy had 22 more marbles than wen she had started . How many games did they play?

Let x = number of games played
x  15 = 22 
22+15= 37

Assume that both Jane and Kathy start with 0 marbles. If Jane wins the first 15 games in a row, she will now have 15 marbles, and Kathy will have 15 marbles. This is because for ever game Jane wins, Kathy needs to hand over a marble. Jane cannot win anymore games. The goal now is to get Kathy to have 22 marbles, since this is 22 greater than zero, which is what she started with.
Kathy currently has 15 marbles, and she needs to get up to 22 marbles. Let x equal the number of games the girls still have to play.
x+(15)=22
x=37
This is not the final answer, though. This is only the number of times Kathy won. Remember that Jane has already won 15 games. You now have to find the total amount of games they played by adding each girl's number of wins together.
37+15=52 games total