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) About Me  (Show Source):
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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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m = total money at start
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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) About Me  (Show Source):
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Assume Gopal had $x to begin with.
First he spent 3%2F5 "of" his money. So that makes $3x%2F5 in expenditure, and hence $x-3x%2F5=2x%2F5 is what he is left with by the end of the first week.
Now the second week he spent 1%2F3 "of" what he was left with. Since he was left with $2x%2F5, what he spent now would be $1%2F3+%2A+2x%2F5 which is equal to $2x%2F15- 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 $3x%2F5+%2B+2x%2F15 which is equal to $%283%2A15%2B2%2A5%29x%2F%285%2A15%29 or $11x%2F15. This also means that now he's left with $x-11x%2F15 or $4x%2F15.
According to the problem, his total expenditure is $110. But we know that this number is instead $11x%2F15. That means $x, or the money that he had very initially, is $15%2A110%2F11 which is $150. And as we found earlier the money that he is left with is $4x%2F15 or $4%2A150%2F15 or $40.

Answer by MathTherapy(10555) About Me  (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: 3%2F5, so fraction remaining after 1st week: matrix%281%2C3%2C+1+-+3%2F5%2C+%22=%22%2C+2%2F5%29
Fraction spent in 2nd week: matrix%281%2C3%2C+1%2F3%2C+of%2C+remainder%29, so fraction remaining after 2nd week: 
With 4%2F15 remaining in the end, it's obvious that matrix%281%2C5%2C+1+-+4%2F15%2C+or%2C+11%2F15%2C+was%2C+spent%29
With $110 and 11%2F15 being amount and fraction spent, respectively, and R and 4%2F15 being amount and fraction remaining, 
respectively, we get the following PROPORTION: 
                                                       11R = 110(4) ------ Cross-multiplying     
                                   Amount remaining, or