PSLE
Elyse spent ¹₁₀ of her money on a sweater and 5 shirts. The sweater cost 2 times as much as each shirt. Elyse spent ²₃ of her remaining money on a necklace. She spent $740 more on the necklace than on the 5 shirts.
(a) What fraction of Elyse's money was spent on each shirt?
(b) How much money did Elyse have at first?
(a)
Cost of 1 shirt = 1 u

Cost of 5 shirts
= 5 x 1 u
= 5 u

Cost of 1 sweater = 2 u

Cost of 1 sweater and 5 shirts
= 2 u + 5 u
= 7 u

Fraction of Elyse's money spent on each shirt
= ¹₇ x ¹₁₀
= ¹₇₀

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

Elyse's remaining money = 63 u

Cost of the necklace
= ²₃ x 63 u
= 42 u

Amount that Elyse spent more on the necklace than on the 5 shirts
= 42 u - 5 u
= 37 u

37 u = 740

1 u = 740 ÷ 37 = 20

¹⁰₁₀ of her money = 10 x 7 u = 70 u

Amount that Elyse had at first
= 70 u
= 70 x 20
= $1400

Answer(s): (a) ¹₇₀ ; (b) $1400