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Answer on Algebra Question for SUNFLOWER

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Question #3221
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?
Expert's answer

Answer

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.

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