Two very unrealistic mathematics problems, yet they can be fun to both explore and solve.
Problem 1: A woman has four cows, for which she gave $800: the first cow cost as much as the second and half of the third, the second cost as much as the fourth minus the cost of the third, the third cost one-third of the first, and the fourth cost as much as the second and third together. What was the price of each cow?
Problem 2: Three men were in a restaurant and decided to split the bill equally between them. By doing so Joe had to pay an extra 15 cents, Jack saved 21 cents. They turned to Tom and said: "What you had would have cost you a dollar sixty-five, so you don't lose much." Can you work out the total bill?
Source: Gyles Brandreth, The Puzzle Mountain, 1981
Hint: Again, try to avoid jumping right into the use of algebra. Can you draw pictures that show the relationships in the first problem? And for the second problem, if you stop and think...carefully...you can figure out the answer (or should I say answers, since the term ""lose much" is troublesome.)
Solution Commentary: No solutions provided...though there are many different solution techniques. Also, you will know the answers when you have them....