PSLE
Esther spent ¹₈ of her money on a shirt and 4 sweaters. The shirt cost 2 times as much as each sweater. Esther spent ²₃ of her remaining money on a necklace. She spent $576 more on the necklace than on the 4 sweaters.
(a) What fraction of Esther's money was spent on each sweater?
(b) How much money did Esther have at first?
(a)
Cost of 1 sweater = 1 u

Cost of 4 sweaters
= 4 x 1 u
= 4 u

Cost of 1 shirt = 2 u

Cost of 1 shirt and 4 sweaters
= 2 u + 4 u
= 6 u

Fraction of Esther's money spent on each sweater
= ¹₆ x ¹₈
= ¹₄₈

(b)
¹₈ of her money = 6 u
⁷₈ of her money = 7 x 6 u = 42 u

Esther's remaining money = 42 u

Cost of the necklace
= ²₃ x 42 u
= 28 u

Amount that Esther spent more on the necklace than on the 4 sweaters
= 28 u - 4 u
= 24 u

24 u = 576

1 u = 576 ÷ 24 = 24

⁸₈ of her money = 8 x 6 u = 48 u

Amount that Esther had at first
= 48 u
= 48 x 24
= $1152

Answer(s): (a) ¹₄₈ ; (b) $1152