2012 AMC 10B Problem 5

Below is the professionally curated solution for Problem 5 of the 2012 AMC 10B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2012 AMC 10B solutions, or check the answer key.

All of the real AMC 8, AMC 10, AMC 12, and AIME problems in our complete solution collection are used with official legal permission of the Mathematical Association of America (MAA).

Concepts:percentage linear equation

Difficulty rating: 900

Anna enjoys dinner at a restaurant in Washington, D.C., where the sales tax on meals is $10\%.$ She leaves a $15\%$ tip on the price of her meal before the sales tax is added, and the tax is calculated on the pre-tip amount. She spends a total of $\$27.50$ for dinner. What is the cost of her dinner without tax or tip in dollars?

$\$18$

$\$20$

$\$21$

$\$22$

$\$24$

Solution:

Suppose the original price is $x.$ Then, the tax is $0.1$ and the tip is $0.15x.$ This makes the total payment equal to: $\begin{align*}x+0.1x+0.15x&=1.25x\\&=27.5\end{align*}$ Therefore, $x=22.$

Thus, the correct answer is D .

← Problem 4 Full Exam Problem 6 →

Problem 5 in Other Years

2000 AMC 10 · 2001 AMC 10 · 2002 AMC 10A · 2002 AMC 10B · 2003 AMC 10A · 2003 AMC 10B · 2004 AMC 10A · 2004 AMC 10B · 2005 AMC 10A · 2005 AMC 10B · 2006 AMC 10A · 2006 AMC 10B · 2007 AMC 10A · 2007 AMC 10B · 2008 AMC 10A · 2008 AMC 10B · 2009 AMC 10A · 2009 AMC 10B · 2010 AMC 10A · 2010 AMC 10B · 2011 AMC 10A · 2011 AMC 10B · 2012 AMC 10A · 2013 AMC 10A · 2013 AMC 10B · 2014 AMC 10A · 2014 AMC 10B · 2015 AMC 10A · 2015 AMC 10B · 2016 AMC 10A · 2016 AMC 10B · 2017 AMC 10A · 2017 AMC 10B · 2018 AMC 10A · 2018 AMC 10B · 2019 AMC 10A · 2019 AMC 10B · 2020 AMC 10A · 2020 AMC 10B · 2021 AMC 10A Spring · 2021 AMC 10B Spring · 2021 AMC 10A Fall · 2021 AMC 10B Fall · 2022 AMC 10A · 2022 AMC 10B · 2023 AMC 10A · 2023 AMC 10B · 2024 AMC 10A · 2024 AMC 10B · 2025 AMC 10A · 2025 AMC 10B