"at the end of the year juan has $52.71 more than 4 times his balance at the beginning of the year if his ending balance was $172.90 what is found at the beginning of the year"

At the end of the year, Juan has 52.71 more than 4 times his balance at the beginning. Okay, let's set this up.

4x + 52.71
(4 times) (52.71 more)
His ending was 172.90, so
4x + 52.71=172.90
4x= 120.19
x= 30.05
He had $30.05 at the beginning of the year.