PSLE
Raeann spent ¹₅ of her money on a vest and 3 sweaters. The vest cost 3 times as much as each sweater. Raeann spent ¹₂ of her remaining money on a ring. She spent $126 more on the ring than on the 3 sweaters.
(a) What fraction of Raeann's money was spent on each sweater?
(b) How much money did Raeann have at first?
(a)
Cost of 1 sweater = 1 u

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

Cost of 1 vest = 3 u

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

Fraction of Raeann's money spent on each sweater
= ¹₆ x ¹₅
= ¹₃₀

(b)
¹₅ of her money = 6 u
⁴₅ of her money = 4 x 6 u = 24 u

Raeann's remaining money = 24 u

Cost of the ring
= ¹₂ x 24 u
= 12 u

Amount that Raeann spent more on the ring than on the 3 sweaters
= 12 u - 3 u
= 9 u

9 u = 126

1 u = 126 ÷ 9 = 14

⁵₅ of her money = 5 x 6 u = 30 u

Amount that Raeann had at first
= 30 u
= 30 x 14
= $420

Answer(s): (a) ¹₃₀ ; (b) $420