Question

Nina has exactly enough money to purchase 6 widgets. If the cost of each widget were reduced by $1.25, then Nina would have exactly enough money to purchase 8 widgets. How much money does Nina have?

Answer 1

x - the amount of money Nina has
y - the cost of one widget

Nina has exactly enough money to purchase 6 widgets.

`x=6y`

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.

`x=8(y-1.25)`

Substitute 6y for x in the second equation:

`6y=8(y-1.25) \\ 6y=8y-10 \\ 6y-8y=-10 \\ -2y=-10 \\ y=(-10)/(-2) \\ y=5 \\ \\ x=6y=6 * 5=30`

Nina has $30.