PSLE
Dana spent ¹₉ of her money on a jumpsuit and 3 vests. The jumpsuit cost 3 times as much as each vest. Dana spent ⁵₈ of her remaining money on a ring. She spent $378 more on the ring than on the 3 vests.
(a) What fraction of Dana's money was spent on each vest?
(b) How much money did Dana have at first?
(a)
Cost of 1 vest = 1 u

Cost of 3 vests
= 3 x 1 u
= 3 u

Cost of 1 jumpsuit = 3 u

Cost of 1 jumpsuit and 3 vests
= 3 u + 3 u
= 6 u

Fraction of Dana's money spent on each vest
= ¹₆ x ¹₉
= ¹₅₄

(b)
¹₉ of her money = 6 u
⁸₉ of her money = 8 x 6 u = 48 u

Dana's remaining money = 48 u

Cost of the ring
= ⁵₈ x 48 u
= 30 u

Amount that Dana spent more on the ring than on the 3 vests
= 30 u - 3 u
= 27 u

27 u = 378

1 u = 378 ÷ 27 = 14

⁹₉ of her money = 9 x 6 u = 54 u

Amount that Dana had at first
= 54 u
= 54 x 14
= $756

Answer(s): (a) ¹₅₄ ; (b) $756