Ivory spent 80% of her money on a number of beads. She spent 20% of the remaining money on a few cards and 50% of what was left on a number of coins.

1. What fraction of her money was left?
2. Given that the beads cost $36 more than the coins, find the sum of money Ivory had at first.

(a)
80% = ⁸⁰₁₀₀ = ⁴₅

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

20% = ²⁰₁₀₀ = ¹₅

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

50% = ⁵⁰₁₀₀ = ¹₂

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

Fraction of money left after buying the beads
= ¹₅ x ⁴₅ x ¹₂
= ²₂₅

(b)
Fraction of money spent on the coins
= ¹₅ x ⁴₅ x ¹₂
= ²₂₅

Fraction of money spent on the beads
= ⁴₅
= ²⁰₂₅

Amount spent more on the beads than the coins
= 20 u - 2 u
= 18 u

18 u = 36

1 u = 36 ÷ 18 = 2

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

Answer(s): (a) ²₂₅; (b) $50