Algebra: Word Problem - Handshakes

At a party I gave, attended only by couples, some persons shook hands. Upon inquiry, I found at the end of the evening that everyone else had shaken a different number of hands. How many hands did my spouse shake? Please be detailed in your response. I need to understand the thought processes involved in this problem.

Algebra: Word Problem - System of Equations

Three people play a game in which one person loses and two people win each game. The one who loses must double the amount of money that each of the other players has at that time. The three players agree to play three games. At the end of the three games, each player has lost one game and each has $8. What was the original st ...continues

Algebra : Word Problem - Sums and Products

During the census, a man told the census-taker that he had three children. When asked their ages he replied, " The product of their ages is 72. The sum of their ages is my house number." The census taker turned around and ran outside to look at the house number displayed over the door. He then re-entered the house and said, " ...continues

Perturbation Theory

Find the real root of the equation x^5 + ex - 1= 0 approximately to O(^2) using perturbation theory.

Perturbation theory

Find the real roots of the equation x^5 + ex-1=0 approximately to O(e^2) usind perturbation theory. Compare the accuracy of the perturbative solution for e=0.001, 0.1, and 1

Customers in a Queue

Customers arrive into a queue, where they are served, and then depart. We model the time between two successive arrivals by an exponential distribution with an arrival rate l=9. Similarly, the departure times are modeled by an exponential distribution with a departure rate m=10. Find the average number of customers in the que ...continues

Problem Solving

A man enters a bank and has a check cashed. The teller mistakes the figures and pays cents for dollars and dollars for cents. The man then pays a bill for $24.11 after which he finds he has twice as much money as the face value of the original check. What was the face value? (In case it makes a difference, this is in US doll ...continues

Algebra : Word Problem - Remainders

A large purse is full of coins. If you count them by 13's, 23's, or 31's, there will be one left over. If you count them by 73's there will be none left over. How many coins are there in the purse? Please be detailed in your response.

Algebra : Remainders

What is the remainder when the product of one hundred 5's is divided by 7? Please be detailed in your response.

Miner and Bickford's Fuse : How to get a Fuse of Specific Length

You are a miner and you have three pieces of Bickford's fuse of equal length. You need only 3/4 of one of them. You have no ruler or other measurement device with you. You cannot also bend the fuses as they are old and can be broken at any point while being bent. You only can ignite them from any end and extinguish at any moment ...continues