PSLE
Lucy spent ¹₁₀ of her money on a dress and 5 sweaters. The dress cost 2 times as much as each sweater. Lucy spent ⁵₆ of her remaining money on a ring. She spent $522.5 more on the ring than on the 5 sweaters.
(a) What fraction of Lucy's money was spent on each sweater?
(b) How much money did Lucy have at first?
(a)
Cost of 1 sweater = 1 u

Cost of 5 sweaters
= 5 x 1 u
= 5 u

Cost of 1 dress = 2 u

Cost of 1 dress and 5 sweaters
= 2 u + 5 u
= 7 u

Fraction of Lucy's money spent on each sweater
= ¹₇ x ¹₁₀
= ¹₇₀

(b)
¹₁₀ of her money = 7 u
⁹₁₀ of her money = 9 x 7 u = 63 u

Lucy's remaining money = 63 u

Cost of the ring
= ⁵₆ x 63 u
= 52.5 u

Amount that Lucy spent more on the ring than on the 5 sweaters
= 52.5 u - 5 u
= 47.5 u

47.5 u = 522.5

1 u = 522.5 ÷ 47.5 = 11

¹⁰₁₀ of her money = 10 x 7 u = 70 u

Amount that Lucy had at first
= 70 u
= 70 x 11
= $770

Answer(s): (a) ¹₇₀ ; (b) $770