SOLUTION: Gopal spent 3/5 of his money in the first week and 1/3 of the remainder in the second week. He spent $110 altogether. How much money did he have left?

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Question 1190614: Gopal spent 3/5 of his money in the first week and 1/3 of the remainder in the second week. He spent $110 altogether. How much money did he have left?
Found 3 solutions by Alan3354, chitrank, MathTherapy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Gopal spent 3/5 of his money in the first week and 1/3 of the remainder in the second week. He spent $110 altogether. How much money did he have left?
------------------
m = total money at start
---
m*(3/5 + (1/3)*(2/5)) = 110
m*(3/5 + (2/15)) = 110
11m/15 = 110
m = $150
150 - 110 = $40 left
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Answer by chitrank(4)   (Show Source): You can put this solution on YOUR website!
Assume Gopal had $ to begin with.
First he spent "of" his money. So that makes $ in expenditure, and hence $ is what he is left with by the end of the first week.
Now the second week he spent "of" what he was left with. Since he was left with $, what he spent now would be $ which is equal to $- his expenditure in the second week.
The total expenditure of these two weeks would be the sum ofwhat he spent in these two weeks which is $ which is equal to $ or $. This also means that now he's left with $ or $.
According to the problem, his total expenditure is $110. But we know that this number is instead $. That means $, or the money that he had very initially, is $ which is $. And as we found earlier the money that he is left with is $ or $ or $.
Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
Gopal spent 3/5 of his money in the first week and 1/3 of the remainder in the second week. He spent $110 altogether. How much money did he have left?
Fraction spent in 1st week: , so fraction remaining after 1st week: 
Fraction spent in 2nd week: , so fraction remaining after 2nd week: 
With  remaining in the end, it's obvious that 
With $110 and  being amount and fraction spent, respectively, and R and  being amount and fraction remaining, 
respectively, we get the following PROPORTION: 
                                                       11R = 110(4) ------ Cross-multiplying     
                                   Amount remaining, or

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