PSLE
Gem spent ¹₆ of her money on a shirt and 3 sweaters. The shirt cost 2 times as much as each sweater. Gem spent ¹₂ of her remaining money on a necklace. She spent $152 more on the necklace than on the 3 sweaters.
(a) What fraction of Gem's money was spent on each sweater?
(b) How much money did Gem have at first?
(a)
Cost of 1 sweater = 1 u

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

Cost of 1 shirt = 2 u

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

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

(b)
¹₆ of her money = 5 u
⁵₆ of her money = 5 x 5 u = 25 u

Gem's remaining money = 25 u

Cost of the necklace
= ¹₂ x 25 u
= 12.5 u

Amount that Gem spent more on the necklace than on the 3 sweaters
= 12.5 u - 3 u
= 9.5 u

9.5 u = 152

1 u = 152 ÷ 9.5 = 16

⁶₆ of her money = 6 x 5 u = 30 u

Amount that Gem had at first
= 30 u
= 30 x 16
= $480

Answer(s): (a) ¹₃₀ ; (b) $480