Question

6) Mrs. Kalinowski bought a new bag for $54. After tax, the total came to $58.59. What was the sales taxrate on the bag?

Answer 1

`\text{ sales tax rate on the bag = 8.5\%}`

Step-by-step explanation:

The cost of the bag = $54

Total cost after sales tax = $58.59

The formula relating the sales tax rate and total cost is given as:

`\text{Total cost after tax = cost (1 + tax rate)}`
`\begin{gathered} 58.59\text{ = }54.59\text{ (1 + tax rate)} \\ \text{divide both sides by }54.59\colon \\ (58.59)/(54)\text{ = }\frac{54\text{ (1 + tax rate)}}{54} \end{gathered}`
`\begin{gathered} (58.59)/(54)\text{ = (1 + tax rate)} \\ 1.08500\text{ = 1 + tax rate} \\ \text{subtract 1 from both sides:} \\ 1.08500\text{ - 1 = tax rate} \end{gathered}`
`\begin{gathered} 0.08500\text{ = tax rate} \\ sales\text{ tax rate = 0.085} \\ \\ In\text{ percentage = 0.085 }*\text{ 100\%} \\ \text{ sales tax rate on the bag = 8.5\%} \end{gathered}`