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
To determine how many games Jane and Kathy played, we can set up an equation based on the given information. Let's assume they played "x" number of games.
Since Jane won 15 times, she received 15 marbles from Kathy. Let's denote the number of marbles Jane had at the start of the game as J. Therefore, at the end of the game, Jane would have J + 15 marbles.
Now, Kathy had 22 more marbles than when she started. Let's denote the number of marbles Kathy had at the start of the game as K. Therefore, at the end of the game, Kathy would have K - 15 marbles.
Given that Kathy had 22 more marbles than her starting amount, we can write the equation K - 15 = K + 22.
Now, let's solve the equation:
K - 15 = K + 22
Subtract K from both sides:
-15 = 22
As you can see, -15 is not equal to 22. Therefore, there is no solution to this equation.
Hence, there seems to be an error in the given information or the relationship between the number of games and the number of marbles won/lost is not accurately defined.