PSLE
Esther spent ¹₈ of her money on a shirt and 5 dresses. The shirt cost 2 times as much as each dress. Esther spent ³₇ of her remaining money on a ring. She spent $176 more on the ring than on the 5 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 5 dresses
= 5 x 1 u
= 5 u

Cost of 1 shirt = 2 u

Cost of 1 shirt and 5 dresses
= 2 u + 5 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 ring
= ³₇ x 49 u
= 21 u

Amount that Esther spent more on the ring than on the 5 dresses
= 21 u - 5 u
= 16 u

16 u = 176

1 u = 176 ÷ 16 = 11

⁸₈ of her money = 8 x 7 u = 56 u

Amount that Esther had at first
= 56 u
= 56 x 11
= $616

Answer(s): (a) ¹₅₆ ; (b) $616