# Answer to Question #3221 in Algebra for SUNFLOWER

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

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.

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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