Gabriella bought ff folders that cost $0.30 each and mm markers that cost $0.60 each. Sales tax is 3%. Which expression represents the total amount Gabriella paid, including tax?

Answer 1

To calculate the total amount Gabriella paid, including tax, we can break down the costs step by step:

1. Calculate the cost of the folders: If Gabriella bought $ff$ folders, and each folder costs $0.30, the total cost for the folders is: $$0.30\times ff$$

2. Calculate the cost of the markers: If Gabriella bought $mm$ markers, and each marker costs $0.60, the total cost for the markers is: $$0.60\times mm$$

3. Calculate the total cost before tax: The total cost before applying the sales tax is the sum of the costs of the folders and markers: $$\text{Total cost before tax}=(0.30\times ff)+(0.60\times mm)$$

4. Calculate the sales tax: The sales tax is 3% of the total cost before tax. To express this as an equation: $$\text{Sales tax}=0.03\times \text{Total cost before tax}$$

5. Express the total amount Gabriella paid, including tax: The total amount including sales tax is given by: $$\text{Total amount}=\text{Total cost before tax}+\text{Sales tax}$$ Substituting the previous expressions gives us: $$\text{Total amount}=(0.30\times ff)+(0.60\times mm)+0.03\times ((0.30\times ff)+(0.60\times mm))$$

6. Factor out the common term: $$\text{Total amount}=(0.30\times ff)+(0.60\times mm)+0.03\times ((0.30\times ff)+(0.60\times mm))=(1+0.03)\times ((0.30\times ff)+(0.60\times mm))=1.03\times ((0.30\times ff)+(0.60\times mm))$$

Thus, the expression that represents the total amount Gabriella paid, including tax, is: $$1.03\times ((0.30\times ff)+(0.60\times mm))$$