PSLE
Diana spent ¹₈ of her money on a windbreaker and 3 dresses. The windbreaker cost 3 times as much as each dress. Diana spent ³₇ of her remaining money on a bracelet. She spent $345 more on the bracelet than on the 3 dresses.
(a) What fraction of Diana's money was spent on each dress?
(b) How much money did Diana have at first?
(a)
Cost of 1 dress = 1 u

Cost of 3 dresses
= 3 x 1 u
= 3 u

Cost of 1 windbreaker = 3 u

Cost of 1 windbreaker and 3 dresses
= 3 u + 3 u
= 6 u

Fraction of Diana's money spent on each dress
= ¹₆ x ¹₈
= ¹₄₈

(b)
¹₈ of her money = 6 u
⁷₈ of her money = 7 x 6 u = 42 u

Diana's remaining money = 42 u

Cost of the bracelet
= ³₇ x 42 u
= 18 u

Amount that Diana spent more on the bracelet than on the 3 dresses
= 18 u - 3 u
= 15 u

15 u = 345

1 u = 345 ÷ 15 = 23

⁸₈ of her money = 8 x 6 u = 48 u

Amount that Diana had at first
= 48 u
= 48 x 23
= $1104

Answer(s): (a) ¹₄₈ ; (b) $1104