To determine the final cost of the desk chair, let's go through each step one by one:
1. Sticker Price: The initial price of the desk chair is [tex]$\$[/tex]100.00[tex]$.
2. Discount Calculation:
- The discount is $[/tex]20\%[tex]$ of the sticker price.
- To find the discount amount, we multiply the sticker price by the discount percentage:
\[
\text{Discount Amount} = 0.20 \times 100 = \$[/tex]20.00
\]
3. Price After Discount:
- Subtract the discount amount from the sticker price to get the price after the discount:
[tex]\[
\text{Price After Discount} = 100 - 20 = \$80.00
\][/tex]
4. Coupon Application:
- The coupon reduces the price by [tex]$\$[/tex]10.00[tex]$.
- Subtracting the coupon value from the price after the discount gives us:
\[
\text{Price After Coupon} = 80 - 10 = \$[/tex]70.00
\]
5. Rebate Application:
- Finally, the mail-in rebate reduces the price further by [tex]$\$[/tex]2.00[tex]$.
- Subtracting the rebate value from the price after applying the coupon gives us:
\[
\text{Final Price} = 70 - 2 = \$[/tex]68.00
\]
Therefore, the final cost of the desk chair, after applying the [tex]$20\%$[/tex] discount, the [tex]$\$[/tex]10.00[tex]$ coupon, and the $[/tex]\[tex]$2.00$[/tex] mail-in rebate, is [tex]$\$[/tex]68.00$.
