PSLE
At first, Ryan had some money. He spent ¹₃ of it on a vest and ³₅ of the remainder on a shirt. After that, his aunt gave him $160. 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 Ryan have at first?
Fraction of the total on remainder
= 1 - ¹₃
= ²₃

Fraction of the remainder on what was left 
= 1 - ³₅
= ²₅

Fraction of the total on what was left
= ²₃ x ²₅
= ⁴₁₅

The total at first is the repeated identity.  Make the total at first the same. LCM of 3 and 15 = 15

Total in the end : Total at first
4_x5 : 3_x5
20 : 15

Amount that his aunt gave him
= 20 u - 4 u
= 16 u

16 u = 160

1 u = 160 ÷ 16 = 10

Amount that Ryan had at first
= 15 u
= 15 x 10
= $150

Answer(s): $150