In Exercises 1-3, set up and solve an appropriate system of linear equations to answer the questions.
1. Grace is three times as old as Hans, but in 5 years she will be twice as old as Hans is then. How old are they now?
2. The sum of Annie's, Bert's, and Chris's ages is 60. Annie is older than Bert by the same number of years that Bert is older than Chris. When Bert is as old as Annie is now, Annie will be three times as old as Chris is now. What are their ages?
3. There are two fields whose total area is 1800 square yards. One field produces grain at the rate of 2/3 bushel per square yard; the other field produces grain at the rate of t bushel per square yard. If the total yield is 1100 bushels, what is the size of each field?
The preceding two problems are typical of those found in popular books of mathematical puzzles. However, they have their origins in antiquity. A Babylonian clay tablet that survives from about 300 B. c. contains the following problem.