PSLE
Emily spent ¹₁₀ of her money on a skirt and 3 vests. The skirt cost 2 times as much as each vest. Emily spent ¹₄ of her remaining money on a ring. She spent $132 more on the ring than on the 3 vests.
(a) What fraction of Emily's money was spent on each vest?
(b) How much money did Emily have at first?
(a)
Cost of 1 vest = 1 u

Cost of 3 vests
= 3 x 1 u
= 3 u

Cost of 1 skirt = 2 u

Cost of 1 skirt and 3 vests
= 2 u + 3 u
= 5 u

Fraction of Emily's money spent on each vest
= ¹₅ x ¹₁₀
= ¹₅₀

(b)
¹₁₀ of her money = 5 u
⁹₁₀ of her money = 9 x 5 u = 45 u

Emily's remaining money = 45 u

Cost of the ring
= ¹₄ x 45 u
= 11.25 u

Amount that Emily spent more on the ring than on the 3 vests
= 11.25 u - 3 u
= 8.25 u

8.25 u = 132

1 u = 132 ÷ 8.25 = 16

¹⁰₁₀ of her money = 10 x 5 u = 50 u

Amount that Emily had at first
= 50 u
= 50 x 16
= $800

Answer(s): (a) ¹₅₀ ; (b) $800