PSLE
Lucy spent ¹₁₀ of her money on a vest and 3 dresses. The vest cost 3 times as much as each dress. Lucy spent ²₃ of her remaining money on a necklace. She spent $693 more on the necklace than on the 3 dresses.
(a) What fraction of Lucy's money was spent on each dress?
(b) How much money did Lucy have at first?
(a)
Cost of 1 dress = 1 u

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

Cost of 1 vest = 3 u

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

Fraction of Lucy's money spent on each dress
= ¹₆ x ¹₁₀
= ¹₆₀

(b)
¹₁₀ of her money = 6 u
⁹₁₀ of her money = 9 x 6 u = 54 u

Lucy's remaining money = 54 u

Cost of the necklace
= ²₃ x 54 u
= 36 u

Amount that Lucy spent more on the necklace than on the 3 dresses
= 36 u - 3 u
= 33 u

33 u = 693

1 u = 693 ÷ 33 = 21

¹⁰₁₀ of her money = 10 x 6 u = 60 u

Amount that Lucy had at first
= 60 u
= 60 x 21
= $1260

Answer(s): (a) ¹₆₀ ; (b) $1260