PSLE
Opal spent ¹₅ of her money on a sweater and 2 dresses. The sweater cost 3 times as much as each dress. Opal spent ¹₂ of her remaining money on a necklace. She spent $120 more on the necklace than on the 2 dresses.
(a) What fraction of Opal's money was spent on each dress?
(b) How much money did Opal have at first?
(a)
Cost of 1 dress = 1 u

Cost of 2 dresses
= 2 x 1 u
= 2 u

Cost of 1 sweater = 3 u

Cost of 1 sweater and 2 dresses
= 3 u + 2 u
= 5 u

Fraction of Opal's money spent on each dress
= ¹₅ x ¹₅
= ¹₂₅

(b)
¹₅ of her money = 5 u
⁴₅ of her money = 4 x 5 u = 20 u

Opal's remaining money = 20 u

Cost of the necklace
= ¹₂ x 20 u
= 10 u

Amount that Opal spent more on the necklace than on the 2 dresses
= 10 u - 2 u
= 8 u

8 u = 120

1 u = 120 ÷ 8 = 15

⁵₅ of her money = 5 x 5 u = 25 u

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

Answer(s): (a) ¹₂₅ ; (b) $375