Dana spent 60% of her money on a number of pens. She spent 25% of the remaining money on a few beads and 50% of what was left on a number of marbles.

1. What fraction of her money was left?
2. Given that the pens cost $27 more than the marbles, find the sum of money Dana had at first.

(a)
60% = ⁶⁰₁₀₀ = ³₅

Fraction of money left after buying the pens = 1 - ³₅ = ²₅

25% = ²⁵₁₀₀ = ¹₄

Fraction of remaining money after buying the beads = 1 - ¹₄ = ³₄ 

50% = ⁵⁰₁₀₀ = ¹₂

Fraction of what is left after buying the marbles = 1 - ¹₂ = ¹₂

Fraction of money left after buying the pens
= ²₅ x ³₄ x ¹₂
= ³₂₀

(b)
Fraction of money spent on the marbles
= ²₅ x ³₄ x ¹₂
= ³₂₀

Fraction of money spent on the pens
= ³₅
= ¹²₂₀

Amount spent more on the pens than the marbles
= 12 u - 3 u
= 9 u

9 u = 27

1 u = 27 ÷ 9 = 3

Amount that Dana had at first
= 20 u
= 20 x 3
= $60

Answer(s): (a) ³₂₀; (b) $60