Final answer:
The part of the expression that represents the amount of tax paid is 0.096(14X), which is the tax rate as a decimal multiplied by the pre-tax cost. The part of the expression 0.096(14X) that represents the amount of tax that must be paid is 0.096.
Step-by-step explanation:
The expression given to calculate the total cost is 14X + 0.096(14X). In this expression, 0.096(14X) represents the amount of tax that must be paid. This is because the percentage of the sales tax is converted to a decimal form by dividing by 100, which turns 9.6% into 0.096. To find the amount of sales tax, we multiply this decimal by the total cost before tax, which is represented by 14X as the cost per square foot of tile multiplied by the number of square feet needed.
The expression 0.096(14X) represents the amount of tax that must be paid. In this expression, 0.096 is the tax rate, and 14X represents the cost of the floor tiles before tax. To find the amount of tax, we multiply the tax rate (0.096) by the cost before tax (14X). For example, if X = 100 square feet, then the cost before tax would be 14(100) = 1400, and the amount of tax would be 0.096(1400) = 134.4. Therefore, the part of the expression 0.096(14X) that represents the amount of tax that must be paid is 0.096.