PSLE
At first, Ivan had some money. He spent ¹₃ of it on a windbreaker and ²₇ of the remainder on a jacket. After that, his father gave him $270. 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 Ivan have at first?
Fraction of the total on remainder
= 1 - ¹₃
= ²₃

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

Fraction of the total on what was left
= ²₃ x ⁵₇
= ¹⁰₂₁

The total at first is the repeated identity.  Make the total at first the same. LCM of 3 and 21 = 21

Total in the end : Total at first
4_x7 : 3_x7
28 : 21

Amount that his father gave him
= 28 u - 10 u
= 18 u

18 u = 270

1 u = 270 ÷ 18 = 15

Amount that Ivan had at first
= 21 u
= 21 x 15
= $315

Answer(s): $315