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Let x be the amount Jillian had saved. She spend a third of it on lunch. So, the remaining amount would e
[tex]x\text{ -}\frac{x}{3}=\frac{2x}{3}[/tex]then she lent 5 to her brother. So, this means that we should subtract 5 from this amount. This leads to
[tex]\frac{2x}{3}\text{ -5}[/tex]we are told that this amount is 16. So we get the equation
[tex]\frac{2x}{3}\text{ -5=16}[/tex]we start by adding 5 on both sides, so we have
[tex]\frac{2x}{3}=16+5=21[/tex]now, we multiply both sides by 3, so we get
[tex]2x=21\cdot3=63[/tex]now we divide both sides by 2, so we get
[tex]x=\frac{63}{2}=31.5[/tex]so Jillian started with 31.5