Fraction P6 2011 PSLE P2 Q18

Faizal had a sum of money. He spent 1/4 of his money on a wallet and 2/5 of the remainder on a book. After that, his parents gave him $120. Finally, the ratio of the amount of money he had in the end to the amount of money he had at first was 5 : 4. What was the sum of money Faizal had at first?


        1        3
1  -  ---  =  ----
        4        4

        2        3
1  -  ---  =  ----
        5        5

 3        3         9
---  x  ----  =  ----
 5        4        20

 9
----  +  $120  -->  5 u
20

1  -->  4 u

  9           9
----  -->  ----  x  4 u  =  1.8 u
20          20

5 u  -  1.8 u  -->  $120

3.2 u  -->  $120

                4
4 u  -->  -----  x  120  =  $150
               3.2


It was $150.

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Alternative solution
------------------------
\<---------------- 4 p --------------->|
[ | | | | ]  [ | | | | ]  [ | | | |]  [ | | | | ]
       [ | | ][ | | ] [ | | ][ | | ][ | | ][   $120   ]
                         |<----------- 5 p ----------->|

5 p  -->  9 u  +  120

4 p --> 20 u

               5
5 p  -->  ----  x  20 u  = 25 u
               4

25 u  -->  9 u  +  120

16 u  -->  120

                20
20 u  -->  ----  x  120  =  $150
                16

It was  $150.