In my left pocket I have a mix of pennies (1 cent) and quarters (25 cents). In my right pocket I have a bunch of dimes (10 cents). The number of coins in each pocket is the same, so is the cash value. What is the smallest (nonzero) number of coins I can have?
What if I had coins of x cents and z cents in my left pocket and coins of y cents in my right pocket - is there some quantitiy of coins I can have so that each pocket has the same number of coins and same cash value? (The value of the coins are positive integers x > y > z.)
Assume I had A coins of x cents and B of z cents in my left pocket and A+B coins of y cents in my right pocket - then
Clearly A=y-z and B= x-y ARE VALID POSITIVE SOLUTIONS