PSLE
Sarah spent ¹₅ of her money on a blazer and 5 sweaters. The blazer cost 2 times as much as each sweater. Sarah spent ³₄ of her remaining money on a ring. She spent $416 more on the ring than on the 5 sweaters.
(a) What fraction of Sarah's money was spent on each sweater?
(b) How much money did Sarah have at first?
(a)
Cost of 1 sweater = 1 u

Cost of 5 sweaters
= 5 x 1 u
= 5 u

Cost of 1 blazer = 2 u

Cost of 1 blazer and 5 sweaters
= 2 u + 5 u
= 7 u

Fraction of Sarah's money spent on each sweater
= ¹₇ x ¹₅
= ¹₃₅

(b)
¹₅ of her money = 7 u
⁴₅ of her money = 4 x 7 u = 28 u

Sarah's remaining money = 28 u

Cost of the ring
= ³₄ x 28 u
= 21 u

Amount that Sarah spent more on the ring than on the 5 sweaters
= 21 u - 5 u
= 16 u

16 u = 416

1 u = 416 ÷ 16 = 26

⁵₅ of her money = 5 x 7 u = 35 u

Amount that Sarah had at first
= 35 u
= 35 x 26
= $910

Answer(s): (a) ¹₃₅ ; (b) $910