PSLE
At first, Liam had some money. He spent ¹₆ of it on a sweater and ²₃ of the remainder on a jacket. After that, his uncle gave him $400. The ratio of the total amount of money he had in the end to the amount of money he had at first was 7 : 6. How much money did Liam have at first?
Fraction of the total on remainder
= 1 - ¹₆
= ⁵₆

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

Fraction of the total on what was left
= ⁵₆ x ¹₃
= ⁵₁₈

The total at first is the repeated identity.  Make the total at first the same. LCM of 6 and 18 = 18

Total in the end : Total at first
7_x3 : 6_x3
21 : 18

Amount that his uncle gave him
= 21 u - 5 u
= 16 u

16 u = 400

1 u = 400 ÷ 16 = 25

Amount that Liam had at first
= 18 u
= 18 x 25
= $450

Answer(s): $450