PSLE
Victoria spent ¹₃ of her money on a jacket and 3 sweaters. The jacket cost 2 times as much as each sweater. Victoria spent ¹₂ of her remaining money on a necklace. She spent $38 more on the necklace than on the 3 sweaters.
(a) What fraction of Victoria's money was spent on each sweater?
(b) How much money did Victoria have at first?
(a)
Cost of 1 sweater = 1 u

Cost of 3 sweaters
= 3 x 1 u
= 3 u

Cost of 1 jacket = 2 u

Cost of 1 jacket and 3 sweaters
= 2 u + 3 u
= 5 u

Fraction of Victoria's money spent on each sweater
= ¹₅ x ¹₃
= ¹₁₅

(b)
¹₃ of her money = 5 u
²₃ of her money = 2 x 5 u = 10 u

Victoria's remaining money = 10 u

Cost of the necklace
= ¹₂ x 10 u
= 5 u

Amount that Victoria spent more on the necklace than on the 3 sweaters
= 5 u - 3 u
= 2 u

2 u = 38

1 u = 38 ÷ 2 = 19

³₃ of her money = 3 x 5 u = 15 u

Amount that Victoria had at first
= 15 u
= 15 x 19
= $285

Answer(s): (a) ¹₁₅ ; (b) $285