Quantitative Mini-Problems (Independent)

Solve each problem independently. Show your setup clearly. Use standard unit conversions and give exact values.

1. Unit conversion: How many 3-inch segments can a 4.5-yard line be divided into?
2. Stock transactions: Alex buys 100 shares at $100 per share. The price rises by 10% and he sells 50 shares. Then the price drops by 10% and he sells the remaining 50 shares. How much money does he receive for the last 50 shares?
3. Cash drawer: A cash drawer contains 160 bills, all $10s and $50s, totaling $2,760. How many $10 bills and how many $50 bills are in the drawer?
4. Time management: A teacher has 4 hours to grade papers from 45 students. She finishes the first 5 papers in 30 minutes. What is the average time available per remaining paper to finish within the 4 hours?
5. Sum of squares: Let m = 1^2 + 2^2 + ... + 512^2. Compute S = 2^2 + 4^2 + 6^2 + ... + 1024^2 in terms of m.