For this case we have the following variable:
p: cost of the item that Arthur wants to buy before tax
The expression for the 6% tax is given by:
[tex] \frac{6}{100} p [/tex]
Or equivalently:
[tex] 0.06p [/tex]
Therefore, two different expressions for the total cost are:
Expression 1:
[tex] p + \frac{6}{100} p [/tex]
Expression 2:
[tex] p + 0.06p [/tex]
To prove that they are equal, suppose that the item costs $ 100:
Expression 1:
[tex] p + \frac{6}{100} p [/tex]
[tex] 100+ \frac{6}{100} 100 [/tex]
[tex] 100 + 6 [/tex]
[tex] 106 [/tex]
Expression 2:
[tex] p + 0.06p [/tex]
[tex] 100 + 0.06 (100) [/tex]
[tex] 100 + 6 [/tex]
[tex] 106 [/tex]
Since the cost is the same, then the expressions are the same.
Answer:
Two different expressions that model the problem are:
[tex] p + \frac{6}{100} p [/tex]
[tex] p + 0.06p [/tex]
