Hi Cheryl,

Suppose the total cost is $T$ doll are and the cost before the taxes are added is $S$ dollars. When you purchase an prices at $S$ dollars then you pay 5% of $S$ dollars as one tax and 9.975% of $S$ dollars as the second tax. Thus you have to pay

\[T = S + 0.05 \times S + 0.09975 \times S = (1 + 0.05 + 0.09975) \times S = 1.14975 \times S.\]

Hence $T = 1.14975 \times S$ and dividing both sides by $1.14975$ you get

\[S = \frac{T}{1.14975.}\]

Now that you know the cost before taxes you can calculate the two taxes as

\[0.05 \times S \mbox{ and } 0.09975 \times S\]

Penny