Zoe paid $\$ 18.60$ in sales tax and tips for her dinner. The sales tax rate is $11 \%$ , and she tipped $20 \%$ . (The sales tax does not apply to the tip, and the tip is based on the price of the dinner before sales tax.) $\newline$ What was the price of Zoe's dinner, before sales tax and tip? $\newline$ $\$$

Full solution

Q. Zoe paid

\$ 18.60

in sales tax and tips for her dinner. The sales tax rate is

11 \%

, and she tipped

20 \%

. (The sales tax does not apply to the tip, and the tip is based on the price of the dinner before sales tax.)

\newline

What was the price of Zoe's dinner, before sales tax and tip?

\newline

\$

Given Information: We know: $\newline$ Total amount paid for sales tax and tips: $\$18.60$ $\newline$ Sales tax rate: $11\%$ $\newline$ Tip percentage: $20\%$ $\newline$ We need to find the price of the dinner before sales tax and tip. $\newline$ Let's denote the price of the dinner before sales tax and tip as $P$ . $\newline$ The sales tax is $11\%$ of $P$ , which is $0.11 \times P$ . $\newline$ The tip is $20\%$ of $P$ , which is $0.20 \times P$ . $\newline$ The total amount paid for sales tax and tips is the sum of the sales tax and the tip. $\newline$ So, $0.11 \times P + 0.20 \times P$ .
Denote Price as $P$ : Combine the percentages to simplify the equation: $\newline$ $0.11P + 0.20P = 0.31P$ $\newline$ Now we have: $\newline$ $0.31P = \$(18.60)$ $\newline$ To find $P$ , we divide $\$18.60$ by $0.31$ : $\newline$ $P = \frac{\$18.60}{0.31}$
Calculate Total Amount: Perform the division to find $P$ : $\newline$ $P = \frac{\$18.60}{0.31}$ $\newline$ $P = \$60$ $\newline$ So, the price of Zoe's dinner before sales tax and tip was $\$60$ .