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Question 1199747: Raj spent 25% of his money on clothes and 1/3 of the remainder on food. After giving $441 to his parents, he was left with 41% of his original sum of money. How much money did he have at first?
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
x = the amount of money, in dollars, Raj starts with
25% = 0.25
25% of x = 0.25x
Raj spent 0.25x dollars on clothes.
He has 0.75x dollars left, ie 75% of his money remains.
1/3 of the remainder = (1/3)*(0.75x)
1/3 of the remainder = (1/3)*((3/4)x)
1/3 of the remainder = (1/4)x
1/3 of the remainder = 0.25x
Raj spent 0.25x dollars on food.
Total amount spent = 0.25x+0.25x = 0.50x
He spent 50%, aka half, of his money on clothes and food combined.
Now subtract off $441 that he gives to his parents.
Raj now has 0.50x-441 dollars.
Set this equal to 0.41x to reflect the idea he has 41% of his original money.
Solve for x.
0.50x-441 = 0.41x
0.50x = 0.41x+441
0.50x-0.41x=441
0.09x=441
x=441/0.09
x=4900
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Check:
25% of $4900 = 0.25*4900 = 1225
Raj spent $1225 on clothes.
Remainder after buying clothes = 4900 - 1225 = 3675
1/3 of remainder = (1/3)*(3675) = 1225
Raj spent $1225 on food.
total spent = clothes+food = 1225+1225 = 2450 dollars.
Now he hands over $441
2450-441 = 2009
Raj is left with $2009
Divide this over the original amount (4900)
2009/4900 = 0.41
this shows Raj has 41% of his original money at this point.
The answer is confirmed.
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Answer: $4900
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