Sam went shopping at a department store. He spent 1/5 of his money on a sofa set and $800 on a washing machine. Later, he spent 1/8 of his remaining amount on dining table. If the amount of money left was $100 more than half of the amount he had at first, how much did Sam have at first?
Let's denote the whole amount of money as X.
Thus 1/5X was sent on a sofa set,
the remaining amount is X - 1/5X - $800 = 4/5X - $800
(4/5X - $800)/8 was spent on dining table
4/5X - $800 - (4/5X - $800)/8 = 7/8* (4/5X - $800)
If the amount of money left was $100 more than half of the amount he had at first :
7/8* (4/5X - $800) - $100 = X/2, let's solve this equation for X.
7/10 X - $700 - $100 = 5X/10
2/10 X = $800
X = $4000
Answser: Sam had $4000 at first.