Emily and sarah had a total of $80. after sarah spent 1/3 of her money and emily spent $17, emily had twice as much money as sarah. how much more money did emily have than sarah at first?

Emily = E
Sarah = S

At the end

E = 2S (Because Emily has double Sarah)
E -> E + 17 (To make up the $17 she spent)
2S -> 3S (Because 2S is two thirds the amount Sarah had, as she spent a third)
E + 17 + 3S = 80 (Because their original amounts were equal to $80)
E + 3S = 63 (Simplifying equation)

I think Emily had 3x as much as Sarah 

╔═⋄═◇═◈═❖═✧═☆═✧═❖═◈═◇═⋄╗✧   ok, now this, is epic.╚═⋄═◇═◈═❖═✧═☆═✧═❖═◈═◇═⋄╝