Mary spent 60% of her money on a number of pens. She spent 20% of the remaining money on a few marbles and 50% of what was left on a number of beads.

1. What fraction of her money was left?
2. Given that the pens cost $77 more than the beads, find the sum of money Mary had at first.

(a)
60% = ⁶⁰₁₀₀ = ³₅

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

20% = ²⁰₁₀₀ = ¹₅

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

50% = ⁵⁰₁₀₀ = ¹₂

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

Fraction of money left after buying the pens
= ²₅ x ⁴₅ x ¹₂
= ⁴₂₅

(b)
Fraction of money spent on the beads
= ²₅ x ⁴₅ x ¹₂
= ⁴₂₅

Fraction of money spent on the pens
= ³₅
= ¹⁵₂₅

Amount spent more on the pens than the beads
= 15 u - 4 u
= 11 u

11 u = 77

1 u = 77 ÷ 11 = 7

Amount that Mary had at first
= 25 u
= 25 x 7
= $175

Answer(s): (a) ⁴₂₅; (b) $175