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?
<pre>Fraction spent in 1st week: {{{3/5}}}, so fraction remaining after 1st week: {{{matrix(1,3, 1 - 3/5, "=", 2/5)}}}
Fraction spent in 2nd week: {{{matrix(1,3, 1/3, of, remainder)}}}, so fraction remaining after 2nd week: {{{matrix(1,9, 1 - 1/3, of, remainder, "=", 2/3, of, 2/5, "=", 4/15)}}}
With {{{4/15}}} remaining in the end, it's obvious that {{{matrix(1,5, 1 - 4/15, or, 11/15, was, spent)}}}
With $110 and {{{11/15}}} being amount and fraction spent, respectively, and R and {{{4/15}}} being amount and fraction remaining, 
respectively, we get the following PROPORTION: {{{matrix(3,3, (11/15)/(4/15), "=", 110/R, (11/15)(15/4), "=", 110/R, 11/4, "=", 110/R)}}}
                                                       11R = 110(4) ------ Cross-multiplying     
                                   Amount remaining, or {{{highlight_green(matrix(1,5, R, "=", 110(4)/11, "=", highlight("$40")))}}}</pre>