x - the amount of money Nina has
y - the cost of one widget
Nina has exactly enough money to purchase 6 widgets.
[tex]x=6y[/tex]
If the cost of each widget was reduced by $1.25 (so the cost of one widget would be y-1.25), Nina would have exactly enough money to purchase 8 widgets.
[tex]x=8(y-1.25)[/tex]
Substitute 6y for x in the second equation:
[tex]6y=8(y-1.25) \\
6y=8y-10 \\
6y-8y=-10 \\
-2y=-10 \\
y=\frac{-10}{-2} \\
y=5 \\ \\
x=6y=6 \times 5=30[/tex]
Nina has $30.
