Wendy spent 80% of her money on a number of pens. She spent 25% of the remaining money on a few coins and 50% of what was left on a number of cards.

1. What fraction of her money was left?
2. Given that the pens cost $58 more than the cards, find the sum of money Wendy had at first.

(a)
80% = ⁸⁰₁₀₀ = ⁴₅

Fraction of money left after buying the pens = 1 - ⁴₅ = ¹₅

25% = ²⁵₁₀₀ = ¹₄

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

50% = ⁵⁰₁₀₀ = ¹₂

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

Fraction of money left after buying the pens
= ¹₅ x ³₄ x ¹₂
= ³₄₀

(b)
Fraction of money spent on the cards
= ¹₅ x ³₄ x ¹₂
= ³₄₀

Fraction of money spent on the pens
= ⁴₅
= ³²₄₀

Amount spent more on the pens than the cards
= 32 u - 3 u
= 29 u

29 u = 58

1 u = 58 ÷ 29 = 2

Amount that Wendy had at first
= 40 u
= 40 x 2
= $80

Answer(s): (a) ³₄₀; (b) $80