You can
put this solution on YOUR website!I would start at the end of the trip and work backwards, like you started to do. She ended up with $13 after spending $7 for lunch. So 13+7 = 20. Prior to that, she spent half of her money on a haircut, so she must have had $40 before the haircut. Now, if she spent 1/5 of her total money on gasoline, leaving $40, then 4/5 of what she started with must have been equal to $40.
Now, see if it works. She started with $50, and she spent 1/5 of it on gas. That means she spent $10 on gas, leaving $40. Next, she spent half of her money that was left on a haircut, which would be $20, leaving her with $20. She spent $7 on lunch leaving her with $13, so it seems to check!
R^2
Dr. Robert J. Rapalje, Retired