PSLE
Gwen spent ¹₄ of her money on a coat and 3 jumpsuits. The coat cost 3 times as much as each jumpsuit. Gwen spent ⁴₅ of her remaining money on a necklace. She spent $319.2 more on the necklace than on the 3 jumpsuits.
(a) What fraction of Gwen's money was spent on each jumpsuit?
(b) How much money did Gwen have at first?
(a)
Cost of 1 jumpsuit = 1 u

Cost of 3 jumpsuits
= 3 x 1 u
= 3 u

Cost of 1 coat = 3 u

Cost of 1 coat and 3 jumpsuits
= 3 u + 3 u
= 6 u

Fraction of Gwen's money spent on each jumpsuit
= ¹₆ x ¹₄
= ¹₂₄

(b)
¹₄ of her money = 6 u
³₄ of her money = 3 x 6 u = 18 u

Gwen's remaining money = 18 u

Cost of the necklace
= ⁴₅ x 18 u
= 14.4 u

Amount that Gwen spent more on the necklace than on the 3 jumpsuits
= 14.4 u - 3 u
= 11.4 u

11.4 u = 319.2

1 u = 319.2 ÷ 11.4 = 28

⁴₄ of her money = 4 x 6 u = 24 u

Amount that Gwen had at first
= 24 u
= 24 x 28
= $672

Answer(s): (a) ¹₂₄ ; (b) $672