PSLE
Cathy spent ¹₉ of her money on a vest and 2 shirts. The vest cost 3 times as much as each shirt. Cathy spent ⁵₈ of her remaining money on a ring. She spent $460 more on the ring than on the 2 shirts.
(a) What fraction of Cathy's money was spent on each shirt?
(b) How much money did Cathy have at first?
(a)
Cost of 1 shirt = 1 u

Cost of 2 shirts
= 2 x 1 u
= 2 u

Cost of 1 vest = 3 u

Cost of 1 vest and 2 shirts
= 3 u + 2 u
= 5 u

Fraction of Cathy's money spent on each shirt
= ¹₅ x ¹₉
= ¹₄₅

(b)
¹₉ of her money = 5 u
⁸₉ of her money = 8 x 5 u = 40 u

Cathy's remaining money = 40 u

Cost of the ring
= ⁵₈ x 40 u
= 25 u

Amount that Cathy spent more on the ring than on the 2 shirts
= 25 u - 2 u
= 23 u

23 u = 460

1 u = 460 ÷ 23 = 20

⁹₉ of her money = 9 x 5 u = 45 u

Amount that Cathy had at first
= 45 u
= 45 x 20
= $900

Answer(s): (a) ¹₄₅ ; (b) $900