PSLE
At first, Nick had some money. He spent ¹₆ of it on a sweater and ²₇ of the remainder on a jumpsuit. After that, his uncle gave him $240. 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 Nick have at first?
Fraction of the total on remainder
= 1 - ¹₆
= ⁵₆

Fraction of the remainder on what was left 
= 1 - ²₇
= ⁵₇

Fraction of the total on what was left
= ⁵₆ x ⁵₇
= ²⁵₄₂

The total at first is the repeated identity.  Make the total at first the same. LCM of 6 and 42 = 42

Total in the end : Total at first
7_x7 : 6_x7
49 : 42

Amount that his uncle gave him
= 49 u - 25 u
= 24 u

24 u = 240

1 u = 240 ÷ 24 = 10

Amount that Nick had at first
= 42 u
= 42 x 10
= $420

Answer(s): $420