PSLE
At first, Elijah had some money. He spent ¹₅ of it on a skirt and ²₃ of the remainder on a vest. After that, his aunt gave him $350. 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 Elijah have at first?
Fraction of the total on remainder
= 1 - ¹₅
= ⁴₅

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

Fraction of the total on what was left
= ⁴₅ x ¹₃
= ⁴₁₅

The total at first is the repeated identity.  Make the total at first the same. LCM of 5 and 15 = 15

Total in the end : Total at first
6_x3 : 5_x3
18 : 15

Amount that his aunt gave him
= 18 u - 4 u
= 14 u

14 u = 350

1 u = 350 ÷ 14 = 25

Amount that Elijah had at first
= 15 u
= 15 x 25
= $375

Answer(s): $375