PSLE
Diana spent ¹₁₀ of her money on a shirt and 5 jackets. The shirt cost 2 times as much as each jacket. Diana spent ⁴₅ of her remaining money on a bracelet. She spent $1225.8 more on the bracelet than on the 5 jackets.
(a) What fraction of Diana's money was spent on each jacket?
(b) How much money did Diana have at first?
(a)
Cost of 1 jacket = 1 u

Cost of 5 jackets
= 5 x 1 u
= 5 u

Cost of 1 shirt = 2 u

Cost of 1 shirt and 5 jackets
= 2 u + 5 u
= 7 u

Fraction of Diana's money spent on each jacket
= ¹₇ x ¹₁₀
= ¹₇₀

(b)
¹₁₀ of her money = 7 u
⁹₁₀ of her money = 9 x 7 u = 63 u

Diana's remaining money = 63 u

Cost of the bracelet
= ⁴₅ x 63 u
= 50.4 u

Amount that Diana spent more on the bracelet than on the 5 jackets
= 50.4 u - 5 u
= 45.4 u

45.4 u = 1225.8

1 u = 1225.8 ÷ 45.4 = 27

¹⁰₁₀ of her money = 10 x 7 u = 70 u

Amount that Diana had at first
= 70 u
= 70 x 27
= $1890

Answer(s): (a) ¹₇₀ ; (b) $1890