PSLE
At first, Cole had some money. He spent ¹₄ of it on a blazer and ³₄ of the remainder on a vest. After that, his aunt gave him $340. The ratio of the total amount of money he had in the end to the amount of money he had at first was 5 : 4. How much money did Cole have at first?
Fraction of the total on remainder
= 1 - ¹₄
= ³₄

Fraction of the remainder on what was left 
= 1 - ³₄
= ¹₄

Fraction of the total on what was left
= ³₄ x ¹₄
= ³₁₆

The total at first is the repeated identity.  Make the total at first the same. LCM of 4 and 16 = 16

Total in the end : Total at first
5_x4 : 4_x4
20 : 16

Amount that his aunt gave him
= 20 u - 3 u
= 17 u

17 u = 340

1 u = 340 ÷ 17 = 20

Amount that Cole had at first
= 16 u
= 16 x 20
= $320

Answer(s): $320