Question

A man who had only pennies gave a beggar half of his money and one penny over. He gave a second beggar half of what was left and one penny over. To a third beggar he gave half of what still remained and four pennies over. He was left with 10 pennies. How much did he begin with?

Answer 1

By working backwards from the 10 pennies the man has left, it can be determined that he originally started with 42 pennies.

Step-by-step explanation:

The question involves a mathematical problem-solving situation where a man starts with an unknown number of pennies and makes a series of transactions, each time giving away half of his remaining money plus a fixed number of pennies. The problem can be solved using algebraic reasoning or working backwards. Since the man is left with 10 pennies after the transactions, we need to determine how much he started with by tracing the steps in reverse.

Steps to solve the problem:

1. He finishes with 10 pennies after giving half and four pennies over. This means before giving to the third beggar, he had (10 - 4) × 2 = 12 pennies.
2. Before giving to the second beggar, he had (12 - 1) × 2 = 22 pennies.
3. The initial amount before giving to the first beggar would be (22 - 1) × 2 = 42 pennies.

The man began with 42 pennies.