Answer
Find out the how much did Sheila have at first .
To proof
Let us assume that the original amount of money be x .
As given
Sheila went shopping and spent $120 on a coat.
Than
money sheila has = x - 120
[tex]She\ then\ used\ \frac{2}{3}\ of\ the\ remaining\ money\ to\ buy\ a\ dress[/tex]
[tex]She\ was\ left\ with\ \frac{1}{5}\ of\ her\ original\ amount\ of\ money.[/tex]
Than the equation becomes
[tex]120 + \frac{2\times(x- 120)}{3} +\frac{1x}{5} = x[/tex]
L.C.M of (5,3) = 15
[tex]1800+{10x -1200 +3x}=15x[/tex]
solving
600 +13x = 15x
600 = 15x - 13x
600 = 2x
[tex]x = \frac{600}{2}[/tex]
x = $300
The shelia have money be $300 .
Hence proved
