PSLE
Xandra spent ¹₅ of her money on a dress and 3 shirts. The dress cost 2 times as much as each shirt. Xandra spent ⁴₅ of her remaining money on a ring. She spent $130 more on the ring than on the 3 shirts.
(a) What fraction of Xandra's money was spent on each shirt?
(b) How much money did Xandra have at first?
(a)
Cost of 1 shirt = 1 u

Cost of 3 shirts
= 3 x 1 u
= 3 u

Cost of 1 dress = 2 u

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

Fraction of Xandra's money spent on each shirt
= ¹₅ x ¹₅
= ¹₂₅

(b)
¹₅ of her money = 5 u
⁴₅ of her money = 4 x 5 u = 20 u

Xandra's remaining money = 20 u

Cost of the ring
= ⁴₅ x 20 u
= 16 u

Amount that Xandra spent more on the ring than on the 3 shirts
= 16 u - 3 u
= 13 u

13 u = 130

1 u = 130 ÷ 13 = 10

⁵₅ of her money = 5 x 5 u = 25 u

Amount that Xandra had at first
= 25 u
= 25 x 10
= $250

Answer(s): (a) ¹₂₅ ; (b) $250