In each game of marbles a loser gives the other player a marble when they finish jane won 15 times, and kathy has 22 more marbles than when she started how many games did they play
G = 15 + 22 = 37 Games played.
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 the number of games played, we can use the information provided.
Let's assume the initial number of marbles Kathy had before playing any games is represented by 'x'.
Since Jane won 15 times, she received 15 marbles from Kathy.
Therefore, the number of marbles Kathy had after playing 15 games can be represented as 'x - 15'.
Given that Kathy has 22 more marbles than when she started, we can set up the following equation:
x - 15 + 22 = x
By simplifying the equation, we get:
x - 15 + 22 - x = 0
-15 + 22 = 0
7 = 0
This equation is not possible, as we obtain an inconsistency.
Therefore, there seems to be an error or missing information in the given problem statement.
To determine how many games Jane and Kathy played, we can use the information provided:
1. Jane won 15 times: This means that Jane received a marble from Kathy 15 times.
2. Kathy has 22 more marbles than when she started: Let's denote the number of marbles Kathy started with as "x." Since Kathy received a marble from Jane 15 times, she would have 15 more marbles. So, Kathy's current number of marbles can be represented as "x + 15."
The difference between Kathy's current number of marbles (x + 15) and her starting number of marbles (x) is given as 22. Therefore, we can set up the equation:
(x + 15) - x = 22
Simplifying the equation, we have:
15 = 22
This equation doesn't hold true because 15 is not equal to 22. Therefore, there seems to be an inconsistency in the information provided. It is not possible to determine the number of games played with the given information.