PSLE
Yen spent ¹₃ of her money on a sweater and 5 blouses. The sweater cost 3 times as much as each blouse. Yen spent ¹₂ of her remaining money on a necklace. She spent $45 more on the necklace than on the 5 blouses.
(a) What fraction of Yen's money was spent on each blouse?
(b) How much money did Yen have at first?
(a)
Cost of 1 blouse = 1 u

Cost of 5 blouses
= 5 x 1 u
= 5 u

Cost of 1 sweater = 3 u

Cost of 1 sweater and 5 blouses
= 3 u + 5 u
= 8 u

Fraction of Yen's money spent on each blouse
= ¹₈ x ¹₃
= ¹₂₄

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

Yen's remaining money = 16 u

Cost of the necklace
= ¹₂ x 16 u
= 8 u

Amount that Yen spent more on the necklace than on the 5 blouses
= 8 u - 5 u
= 3 u

3 u = 45

1 u = 45 ÷ 3 = 15

³₃ of her money = 3 x 8 u = 24 u

Amount that Yen had at first
= 24 u
= 24 x 15
= $360

Answer(s): (a) ¹₂₄ ; (b) $360