PSLE
At first, Tim had some money. He spent ¹₅ of it on a jacket and ³₅ of the remainder on a windbreaker. After that, his uncle gave him $110. The ratio of the total amount of money he had in the end to the amount of money he had at first was 6 : 5. How much money did Tim have at first?
Fraction of the total on remainder
= 1 - ¹₅
= ⁴₅

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

Fraction of the total on what was left
= ⁴₅ x ²₅
= ⁸₂₅

The total at first is the repeated identity.  Make the total at first the same. LCM of 5 and 25 = 25

Total in the end : Total at first
6_x5 : 5_x5
30 : 25

Amount that his uncle gave him
= 30 u - 8 u
= 22 u

22 u = 110

1 u = 110 ÷ 22 = 5

Amount that Tim had at first
= 25 u
= 25 x 5
= $125

Answer(s): $125