PSLE
Diana spent ¹₃ of her money on a vest and 5 blazers. The vest cost 3 times as much as each blazer. Diana spent ³₅ of her remaining money on a necklace. She spent $92 more on the necklace than on the 5 blazers.
(a) What fraction of Diana's money was spent on each blazer?
(b) How much money did Diana have at first?
(a)
Cost of 1 blazer = 1 u

Cost of 5 blazers
= 5 x 1 u
= 5 u

Cost of 1 vest = 3 u

Cost of 1 vest and 5 blazers
= 3 u + 5 u
= 8 u

Fraction of Diana's money spent on each blazer
= ¹₈ x ¹₃
= ¹₂₄

(b)
¹₃ of her money = 8 u
²₃ of her money = 2 x 8 u = 16 u

Diana's remaining money = 16 u

Cost of the necklace
= ³₅ x 16 u
= 9.6 u

Amount that Diana spent more on the necklace than on the 5 blazers
= 9.6 u - 5 u
= 4.6 u

4.6 u = 92

1 u = 92 ÷ 4.6 = 20

³₃ of her money = 3 x 8 u = 24 u

Amount that Diana had at first
= 24 u
= 24 x 20
= $480

Answer(s): (a) ¹₂₄ ; (b) $480