PSLE
At first, Oscar had some money. He spent ¹₃ of it on a sweater and ²₃ of the remainder on a dress. After that, his mother gave him $100. The ratio of the total amount of money he had in the end to the amount of money he had at first was 4 : 3. How much money did Oscar have at first?
Fraction of the total on remainder
= 1 - ¹₃
= ²₃

Fraction of the remainder on what was left 
= 1 - ²₃
= ¹₃

Fraction of the total on what was left
= ²₃ x ¹₃
= ²₉

The total at first is the repeated identity.  Make the total at first the same. LCM of 3 and 9 = 9

Total in the end : Total at first
4_x3 : 3_x3
12 : 9

Amount that his mother gave him
= 12 u - 2 u
= 10 u

10 u = 100

1 u = 100 ÷ 10 = 10

Amount that Oscar had at first
= 9 u
= 9 x 10
= $90

Answer(s): $90