PSLE
Lucy spent ¹₄ of her money on a dress and 4 coats. The dress cost 3 times as much as each coat. Lucy spent ²₃ of her remaining money on a necklace. She spent $240 more on the necklace than on the 4 coats.
(a) What fraction of Lucy's money was spent on each coat?
(b) How much money did Lucy have at first?
(a)
Cost of 1 coat = 1 u

Cost of 4 coats
= 4 x 1 u
= 4 u

Cost of 1 dress = 3 u

Cost of 1 dress and 4 coats
= 3 u + 4 u
= 7 u

Fraction of Lucy's money spent on each coat
= ¹₇ x ¹₄
= ¹₂₈

(b)
¹₄ of her money = 7 u
³₄ of her money = 3 x 7 u = 21 u

Lucy's remaining money = 21 u

Cost of the necklace
= ²₃ x 21 u
= 14 u

Amount that Lucy spent more on the necklace than on the 4 coats
= 14 u - 4 u
= 10 u

10 u = 240

1 u = 240 ÷ 10 = 24

⁴₄ of her money = 4 x 7 u = 28 u

Amount that Lucy had at first
= 28 u
= 28 x 24
= $672

Answer(s): (a) ¹₂₈ ; (b) $672