PSLE
Rachel spent ¹₄ of her money on a sweater and 5 jumpsuits. The sweater cost 3 times as much as each jumpsuit. Rachel spent ⁵₈ of her remaining money on a bracelet. She spent $140 more on the bracelet than on the 5 jumpsuits.
(a) What fraction of Rachel's money was spent on each jumpsuit?
(b) How much money did Rachel have at first?
(a)
Cost of 1 jumpsuit = 1 u

Cost of 5 jumpsuits
= 5 x 1 u
= 5 u

Cost of 1 sweater = 3 u

Cost of 1 sweater and 5 jumpsuits
= 3 u + 5 u
= 8 u

Fraction of Rachel's money spent on each jumpsuit
= ¹₈ x ¹₄
= ¹₃₂

(b)
¹₄ of her money = 8 u
³₄ of her money = 3 x 8 u = 24 u

Rachel's remaining money = 24 u

Cost of the bracelet
= ⁵₈ x 24 u
= 15 u

Amount that Rachel spent more on the bracelet than on the 5 jumpsuits
= 15 u - 5 u
= 10 u

10 u = 140

1 u = 140 ÷ 10 = 14

⁴₄ of her money = 4 x 8 u = 32 u

Amount that Rachel had at first
= 32 u
= 32 x 14
= $448

Answer(s): (a) ¹₃₂ ; (b) $448