2005 AMC 10A Problems/Problem 1

Problem

While eating out, Mike and Joe each tipped their server $$2$. Mike tipped $10\%$ of his bill and Joe tipped $20\%$ of his bill. What was the difference, in dollars, between their bills?

$\textbf{(A) } 2\qquad \textbf{(B) } 4\qquad \textbf{(C) } 5\qquad \textbf{(D) } 10\qquad \textbf{(E) } 20$

Solution

Let $m$ be Mike's bill and $j$ be Joe's bill (both in dollars). We then have $\frac{10}{100}m = 2 \iff m = 20$ and $\frac{20}{100}j = 2 \iff j = 10$, so the desired difference is $\left\lvert m-j\right\rvert = 20-10 = \boxed{\textbf{(D) } 10}$.

Video Solution 1

https://youtu.be/OT47ZnF5MPY

Video Solution 2

https://youtu.be/mApPRP9v_XE

~Charles3829

See Also

2005 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 10 Problems and Solutions

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