My son's math book key gives a different answer than what my wife and I consider the right answer. We both worked independently with our son and I asked two other people (both of whom came to the same conclusion). What's important here is that either we need to be corrected or our son needs to know he can trust in our abilities to help him learn math.
Your friend spends one third of her money on lunch. You then give her \$2.50 to repay a loan. After school, your friend spends \$4.00 for a movie and \$2.50 for a snack. She has \$4.90 left. How much money did she have before lunch?
I worked it out this way:
2/3m + 2.50 (loan repayment) - 4.00 - 2.50 = 4.90
2/3m - 4.00 - 2.50 = 4.90 - 2.50 = 2.40 (cancelling out the loan repayment)
2/3m = 2.40 + 4.00 + 2.50 = 8.90
8.90 / 2 = 4.45
4.45 * 3 = 13.35 = m
Your answer is correct; the only critique I have with the way you have written it would be to write $2/3$ in parentheses (i.e., $(2/3)m$ instead of $2/3m$) to avoid confusion with whether $m$ is mulitplying or dividing.