PSLE
Emily spent ¹₃ of her money on a blazer and 5 coats. The blazer cost 3 times as much as each coat. Emily spent ¹₂ of her remaining money on a necklace. She spent $87 more on the necklace than on the 5 coats.
(a) What fraction of Emily's money was spent on each coat?
(b) How much money did Emily have at first?
(a)
Cost of 1 coat = 1 u

Cost of 5 coats
= 5 x 1 u
= 5 u

Cost of 1 blazer = 3 u

Cost of 1 blazer and 5 coats
= 3 u + 5 u
= 8 u

Fraction of Emily's money spent on each coat
= ¹₈ x ¹₃
= ¹₂₄

(b)
¹₃ of her money = 8 u
²₃ of her money = 2 x 8 u = 16 u

Emily's remaining money = 16 u

Cost of the necklace
= ¹₂ x 16 u
= 8 u

Amount that Emily spent more on the necklace than on the 5 coats
= 8 u - 5 u
= 3 u

3 u = 87

1 u = 87 ÷ 3 = 29

³₃ of her money = 3 x 8 u = 24 u

Amount that Emily had at first
= 24 u
= 24 x 29
= $696

Answer(s): (a) ¹₂₄ ; (b) $696