PSLE
Emma spent ¹₉ of her money on a vest and 4 coats. The vest cost 3 times as much as each coat. Emma spent ¹₄ of her remaining money on a necklace. She spent $130 more on the necklace than on the 4 coats.
(a) What fraction of Emma's money was spent on each coat?
(b) How much money did Emma have at first?
(a)
Cost of 1 coat = 1 u

Cost of 4 coats
= 4 x 1 u
= 4 u

Cost of 1 vest = 3 u

Cost of 1 vest and 4 coats
= 3 u + 4 u
= 7 u

Fraction of Emma's money spent on each coat
= ¹₇ x ¹₉
= ¹₆₃

(b)
¹₉ of her money = 7 u
⁸₉ of her money = 8 x 7 u = 56 u

Emma's remaining money = 56 u

Cost of the necklace
= ¹₄ x 56 u
= 14 u

Amount that Emma spent more on the necklace than on the 4 coats
= 14 u - 4 u
= 10 u

10 u = 130

1 u = 130 ÷ 10 = 13

⁹₉ of her money = 9 x 7 u = 63 u

Amount that Emma had at first
= 63 u
= 63 x 13
= $819

Answer(s): (a) ¹₆₃ ; (b) $819