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Philip and Mark each had an equal amount of money at first. After Philip spent $50 and Mark spent 1/3 of his money, the ratio of Philip's money to Mark' money was 5 : 4. How much money had Philip left?

 Aug 11, 2021
 #1
avatar+780 
+1

$\frac{p-50}{m-\frac{1}{3}m} = \frac{5}{4}$

$\frac{p-50}{\frac{2}{3}m} = \frac{5}{4}$

$p-50(4) = 5 \frac{2}{3}m$

$4p - 200 = \frac{10}{3}m$

$2p - 100 = \frac{5}{3}m$

$6p - 300 = 5m$

Remember: $p = m$

$6p - 300 = 5p$

$p = 300$

$300 - 50 = \boxed{250}$

 Aug 11, 2021
 #2
avatar+272 
+1

               Let:

Before: 

                Philip's money = x dollars

                                                       ]

                Mark's money = x dollars 


After: Accoriding to question:

          Philip's money = (x - 50)  dollars

          Mark's  money = ( x - \(xx {1 \over 3}{}{}\)) = \( {2x \over 3}{}{}\)dollars
 

 

 

 

                According to question:                 
                   x-50/2x/3 = 5/4

                   3 (x-50)/2x = 5/4

                   3x-150/2x 5/4

                  12x - 600 = 10x

                   12x - 10x = 600

                              2x = 600

                                x = 300 dollars

So,

        Philip had remaining money = x - 50 = 300 - 50 = $250

 Aug 11, 2021

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