PSLE
Diana spent ¹₅ of her money on a jacket and 3 sweaters. The jacket cost 2 times as much as each sweater. Diana spent ³₄ of her remaining money on a bracelet. She spent $360 more on the bracelet than on the 3 sweaters.
(a) What fraction of Diana's money was spent on each sweater?
(b) How much money did Diana have at first?
(a)
Cost of 1 sweater = 1 u

Cost of 3 sweaters
= 3 x 1 u
= 3 u

Cost of 1 jacket = 2 u

Cost of 1 jacket and 3 sweaters
= 2 u + 3 u
= 5 u

Fraction of Diana's money spent on each sweater
= ¹₅ x ¹₅
= ¹₂₅

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

Diana's remaining money = 20 u

Cost of the bracelet
= ³₄ x 20 u
= 15 u

Amount that Diana spent more on the bracelet than on the 3 sweaters
= 15 u - 3 u
= 12 u

12 u = 360

1 u = 360 ÷ 12 = 30

⁵₅ of her money = 5 x 5 u = 25 u

Amount that Diana had at first
= 25 u
= 25 x 30
= $750

Answer(s): (a) ¹₂₅ ; (b) $750