PSLE
Emma spent ¹₅ of her money on a vest and 2 dresses. The vest cost 3 times as much as each dress. Emma spent ³₄ of her remaining money on a ring. She spent $130 more on the ring than on the 2 dresses.
(a) What fraction of Emma's money was spent on each dress?
(b) How much money did Emma have at first?
(a)
Cost of 1 dress = 1 u

Cost of 2 dresses
= 2 x 1 u
= 2 u

Cost of 1 vest = 3 u

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

Fraction of Emma's money spent on each dress
= ¹₅ x ¹₅
= ¹₂₅

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

Emma's remaining money = 20 u

Cost of the ring
= ³₄ x 20 u
= 15 u

Amount that Emma spent more on the ring than on the 2 dresses
= 15 u - 2 u
= 13 u

13 u = 130

1 u = 130 ÷ 13 = 10

⁵₅ of her money = 5 x 5 u = 25 u

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

Answer(s): (a) ¹₂₅ ; (b) $250