Suppose we have a number x, and we want to calculate the y% of x. Let's denote this number by z. Then, z is given by the formula
[tex]z=\frac{y\text{\%}}{100}\cdot x\text{.}[/tex]a) In this case, our x is 39.99 and our z is 10. We want to calculate what percentage of 39.99 represents 10. Applying our formula, we get
[tex]10=\frac{y\text{\%}}{100}39.99.[/tex]Solving it for y%, we get
[tex]\begin{gathered} 10=\frac{y\text{\%}}{100}39.99, \\ 10\cdot100=y\text{\%}\cdot39.99, \\ 1000=y\text{\%}\cdot39.99, \\ y\text{\%}=\frac{1000}{39.99}\approx25. \end{gathered}[/tex]b) (Calculated over the original price)
[tex]\begin{gathered} 1.95=\frac{y\text{\%}}{100}\cdot39.99, \\ 1.95\cdot100=y\text{\%}\cdot39.99, \\ 195=y\text{\%}\cdot39.99, \\ y\text{\%}=\frac{195}{39.99}, \\ y\text{\%}\approx4.9. \end{gathered}[/tex]c) Here, we must calculate the percentage of the markup after the discount. The given percentage of the markup is for the original price (39.99). Then, we need to apply our formula two times: the first time to calculate the exact value of the 60% of the original price, and the second one to calculate what is the percentage of this value minus the discount over the subtotal (29.99).
First time)
[tex]\begin{gathered} z=\frac{60}{100}\cdot39.99, \\ z=23.994. \end{gathered}[/tex]Second time)
[tex]\begin{gathered} 23.994-10=\frac{y\text{\%}}{100}\cdot29.99, \\ 13.994\cdot100=y\text{\%}\cdot29.99, \\ 1399.4=y\text{\%}\cdot29.99, \\ y\text{\%}=\frac{1399.4}{29.99}\approx47. \end{gathered}[/tex]Answera) The discount (10) is approximately 25% of the original price (39.99) of the jeans.
b) The sales tax is approximately (rounded to the nearest tenth) 4.9% of the original price of the jeans.
c) After the discount, the markup is approximately 47%.