PSLE
Dana spent ¹₇ of her money on a shirt and 3 dresses. The shirt cost 3 times as much as each dress. Dana spent ¹₃ of her remaining money on a bracelet. She spent $180 more on the bracelet than on the 3 dresses.
(a) What fraction of Dana's money was spent on each dress?
(b) How much money did Dana have at first?
(a)
Cost of 1 dress = 1 u

Cost of 3 dresses
= 3 x 1 u
= 3 u

Cost of 1 shirt = 3 u

Cost of 1 shirt and 3 dresses
= 3 u + 3 u
= 6 u

Fraction of Dana's money spent on each dress
= ¹₆ x ¹₇
= ¹₄₂

(b)
¹₇ of her money = 6 u
⁶₇ of her money = 6 x 6 u = 36 u

Dana's remaining money = 36 u

Cost of the bracelet
= ¹₃ x 36 u
= 12 u

Amount that Dana spent more on the bracelet than on the 3 dresses
= 12 u - 3 u
= 9 u

9 u = 180

1 u = 180 ÷ 9 = 20

⁷₇ of her money = 7 x 6 u = 42 u

Amount that Dana had at first
= 42 u
= 42 x 20
= $840

Answer(s): (a) ¹₄₂ ; (b) $840