2005 AMC 10A Problem 1

Question

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?

2

4

5

10

20

A tip equal to

10\%

of a bill means the bill is

10

times the tip

Recover each bill from its tip, then subtract

Mike’s

\$2

tip is

10\%

of his bill, so his bill is

2 \times 10 = 20

dollars. Joe’s

\$2

tip is

20\%

of his bill, so his bill is

2 \times 5 = 10

dollars. The difference is

20 - 10 = 10

dollars.

Thus, the correct answer is D.

Problem 1 in other years