Solve the following problems:
1. A corporation allows each of its traveling employees an daily meal allowance and a nightly hotel allowance. One employee travels 4 days and 4 nights and is allotted $480. Another employee travels for 3 days and 2 nights and is allotted $270. What is the daily meal allowance and the nightly hotel allowance?
2. One-half of the boys and one-third of the girls of a High School attended the homecoming game, whereas one-third of the boys and one-half of the girls attended the homecoming dance. If there were 570 students at the game and 580 at the dance, then how many students are there at the High School?
3. You want to buy T-shirts and shorts. T-shirts cost $10 each and shorts cost $15 each. If you have $90 to buy a total of 8 T-shirts and shorts, how many of each can you buy?
Word problems are solved using systems of equations. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.