Zara spent 60% of her money on a number of pens. She spent 30% of the remaining money on a few stamps and 50% of what was left on a number of coins.

1. What fraction of her money was left?
2. Given that the pens cost $69 more than the coins, find the sum of money Zara had at first.

(a)
60% = ⁶⁰₁₀₀ = ³₅

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

30% = ³⁰₁₀₀ = ³₁₀

Fraction of remaining money after buying the stamps = 1 - ³₁₀ = ⁷₁₀ 

50% = ⁵⁰₁₀₀ = ¹₂

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

Fraction of money left after buying the pens
= ²₅ x ⁷₁₀ x ¹₂
= ⁷₅₀

(b)
Fraction of money spent on the coins
= ²₅ x ⁷₁₀ x ¹₂
= ⁷₅₀

Fraction of money spent on the pens
= ³₅
= ³⁰₅₀

Amount spent more on the pens than the coins
= 30 u - 7 u
= 23 u

23 u = 69

1 u = 69 ÷ 23 = 3

Amount that Zara had at first
= 50 u
= 50 x 3
= $150

Answer(s): (a) ⁷₅₀; (b) $150