PSLE
Vanessa spent ¹₃ of her money on a skirt and 5 shirts. The skirt cost 2 times as much as each shirt. Vanessa spent ⁵₈ of her remaining money on a ring. She spent $41.25 more on the ring than on the 5 shirts.
(a) What fraction of Vanessa's money was spent on each shirt?
(b) How much money did Vanessa have at first?
(a)
Cost of 1 shirt = 1 u

Cost of 5 shirts
= 5 x 1 u
= 5 u

Cost of 1 skirt = 2 u

Cost of 1 skirt and 5 shirts
= 2 u + 5 u
= 7 u

Fraction of Vanessa's money spent on each shirt
= ¹₇ x ¹₃
= ¹₂₁

(b)
¹₃ of her money = 7 u
²₃ of her money = 2 x 7 u = 14 u

Vanessa's remaining money = 14 u

Cost of the ring
= ⁵₈ x 14 u
= 8.75 u

Amount that Vanessa spent more on the ring than on the 5 shirts
= 8.75 u - 5 u
= 3.75 u

3.75 u = 41.25

1 u = 41.25 ÷ 3.75 = 11

³₃ of her money = 3 x 7 u = 21 u

Amount that Vanessa had at first
= 21 u
= 21 x 11
= $231

Answer(s): (a) ¹₂₁ ; (b) $231