Kimberly spent 70% of her money on a number of marbles. She spent 20% of the remaining money on a few beads and 50% of what was left on a number of pens.

1. What fraction of her money was left?
2. Given that the marbles cost $29 more than the pens, find the sum of money Kimberly had at first.

(a)
70% = ⁷⁰₁₀₀ = ⁷₁₀

Fraction of money left after buying the marbles = 1 - ⁷₁₀ = ³₁₀

20% = ²⁰₁₀₀ = ¹₅

Fraction of remaining money after buying the beads = 1 - ¹₅ = ⁴₅ 

50% = ⁵⁰₁₀₀ = ¹₂

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

Fraction of money left after buying the marbles
= ³₁₀ x ⁴₅ x ¹₂
= ³₂₅

(b)
Fraction of money spent on the pens
= ³₁₀ x ⁴₅ x ¹₂
= ³₂₅

Fraction of money spent on the marbles
= ⁷₁₀
= ³⁵₅₀

Amount spent more on the marbles than the pens
= 17.5 u - 3 u
= 14.5 u

14.5 u = 29

1 u = 29 ÷ 14.5 = 2

Amount that Kimberly had at first
= 25 u
= 25 x 2
= $50

Answer(s): (a) ³₂₅; (b) $50