Your sister and you decided to partner on a car washing endeavor, where you charge cars $10 for a car wash and split the earnings. Since you are doing this at your parent's house and they had extra soap, sponges, and a hose available, there are no costs to you. At the end of the first day, you have earned $45 and she had only earned $10. She claimed that you did not pay her the full payment she deserved. Her argument was: ``If we wash a car, you earn $5 and I earn $5. If you earned $45, then we washed nine cars. If we wash nine cars, I have earned $45. I have earned $10; therefore, you did not give me all of the money that I earned.''First, explain which states that she made that she could not correctly conclude and explain why. Second, counter her argument, using everyday English. The last sentence of your argument should be ``Therefore, I $45 and you earned $10. Third, write this counter-argument using logic statements by first listing the logic statements then writing the argument mathematically.