jmc

Question

A pirate is counting the loot he has stolen from S.S. AOPS, on which everything is counted in base 5. A treasure chest contains 3124_5 dollars worth of jewelry, 3122_5 dollars worth of gold coins, and 124_5 dollars worth of rubbing alcohol. What is the total dollar amount that this pirate has accumulated? Express your answer in base 10.

Accepted Answer

We would like to find 3124_5+3122_5+124_5. 3124_5 = 45^0+25^1+15^2+35^3 = 4+10+25+375 = 414 3122_5 = 25^0+25^1+15^2+35^3 = 2+10+25+375 = 412 124_5 = 45^0+25^1+15^2 = 4+10+25 = 39 Summing all of these together yields 414+412+39= 865 dollars.