PSLE
Cindy spent ¹₇ of her money on a skirt and 2 sweaters. The skirt cost 3 times as much as each sweater. Cindy spent ³₄ of her remaining money on a necklace. She spent $492 more on the necklace than on the 2 sweaters.
(a) What fraction of Cindy's money was spent on each sweater?
(b) How much money did Cindy have at first?
(a)
Cost of 1 sweater = 1 u

Cost of 2 sweaters
= 2 x 1 u
= 2 u

Cost of 1 skirt = 3 u

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

Fraction of Cindy's money spent on each sweater
= ¹₅ x ¹₇
= ¹₃₅

(b)
¹₇ of her money = 5 u
⁶₇ of her money = 6 x 5 u = 30 u

Cindy's remaining money = 30 u

Cost of the necklace
= ³₄ x 30 u
= 22.5 u

Amount that Cindy spent more on the necklace than on the 2 sweaters
= 22.5 u - 2 u
= 20.5 u

20.5 u = 492

1 u = 492 ÷ 20.5 = 24

⁷₇ of her money = 7 x 5 u = 35 u

Amount that Cindy had at first
= 35 u
= 35 x 24
= $840

Answer(s): (a) ¹₃₅ ; (b) $840