College Algebra Problem

Historical math problems can be solved using the college algebra techniques we are learning this semester. (It is NOT necessary to do any sort of research to solve the historical math problems.) Given a word problem, solve it, and write a careful explanation. 

There are often multiple ways to solve a problem. Be sure to show how to solve the problem using algebra. (Define any variables used, write appropriate equation(s), solve them, and show the check of the results.)

 

 

A problem from mathematician Fibonacci in 1202:

A man left to his oldest son 1 bezant and 1/7 of what was left; then, from the remainder, to his next son he
left 2 bezants and 1/7 of what was left; then, from the new remainder, to his third son he left 3 bezants and
1/7 of what was left. He continued this way, giving each son 1 bezant more than the previous son and 1/7
of what remained. By this division, it developed that the last son received all that was left and all the sons
shared equally. How many sons were there and how large was the man’s estate?