Trace: • inheritance
wiki:donuts:springsummer2014:inheritance
Answer
Sandy has $384615 and Sue has $538461
Let X and Y be Sandy's and Sue's money. Let Z be the number of dollars Sandy's statement.
X+Z = Y-Z and 2(X-Z) = Y+Z
X = 5Z
Y = 7Z
Let A be the first digit in Sue's wealth, B be the remaining digits, and n be the number of digits
Y = 10(n-1)A+B
X = 10B + A
7X = 5Y
7(10B+A) = 5(10(n-1)A+B)
(5*10(n-1)-7)A=65B
Since 65B is divisible by 5 and 5*10(n-1)-7 is not, A must equal 5
5*10(n-1)-7 = 13B
The least value of n such that 5*10^(n-1)-7 is a multiple of 13 is 6:
499993=38461*13
The next is 12, which makes them have more than 1 million dollars. Hence n=6, B=38461
wiki/donuts/springsummer2014/inheritance.txt · Last modified: 2014/05/23 13:52 by jmb438