PSLE
Esther spent ¹₈ of her money on a sweater and 4 dresses. The sweater cost 3 times as much as each dress. Esther spent ¹₄ of her remaining money on a necklace. She spent $148.5 more on the necklace than on the 4 dresses.
(a) What fraction of Esther's money was spent on each dress?
(b) How much money did Esther have at first?
(a)
Cost of 1 dress = 1 u

Cost of 4 dresses
= 4 x 1 u
= 4 u

Cost of 1 sweater = 3 u

Cost of 1 sweater and 4 dresses
= 3 u + 4 u
= 7 u

Fraction of Esther's money spent on each dress
= ¹₇ x ¹₈
= ¹₅₆

(b)
¹₈ of her money = 7 u
⁷₈ of her money = 7 x 7 u = 49 u

Esther's remaining money = 49 u

Cost of the necklace
= ¹₄ x 49 u
= 12.25 u

Amount that Esther spent more on the necklace than on the 4 dresses
= 12.25 u - 4 u
= 8.25 u

8.25 u = 148.5

1 u = 148.5 ÷ 8.25 = 18

⁸₈ of her money = 8 x 7 u = 56 u

Amount that Esther had at first
= 56 u
= 56 x 18
= $1008

Answer(s): (a) ¹₅₆ ; (b) $1008