PSLE
Olivia spent ¹₉ of her money on a shirt and 4 skirts. The shirt cost 3 times as much as each skirt. Olivia spent ¹₂ of her remaining money on a ring. She spent $240 more on the ring than on the 4 skirts.
(a) What fraction of Olivia's money was spent on each skirt?
(b) How much money did Olivia have at first?
(a)
Cost of 1 skirt = 1 u

Cost of 4 skirts
= 4 x 1 u
= 4 u

Cost of 1 shirt = 3 u

Cost of 1 shirt and 4 skirts
= 3 u + 4 u
= 7 u

Fraction of Olivia's money spent on each skirt
= ¹₇ x ¹₉
= ¹₆₃

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

Olivia's remaining money = 56 u

Cost of the ring
= ¹₂ x 56 u
= 28 u

Amount that Olivia spent more on the ring than on the 4 skirts
= 28 u - 4 u
= 24 u

24 u = 240

1 u = 240 ÷ 24 = 10

⁹₉ of her money = 9 x 7 u = 63 u

Amount that Olivia had at first
= 63 u
= 63 x 10
= $630

Answer(s): (a) ¹₆₃ ; (b) $630