Difference between revisions of "2006 AMC 10B Problems/Problem 13"
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After drinking and adding cream, Joe's cup has <math>2</math> ounces of cream. | After drinking and adding cream, Joe's cup has <math>2</math> ounces of cream. | ||
− | After adding cream to her cup, JoAnn's cup had <math>14</math> ounces of liquid. By drinking <math>2</math> ounces out of the <math>14</math> ounces of liquid, she drank | + | After adding cream to her cup, JoAnn's cup had <math>14</math> ounces of liquid. By stirring and then drinking <math>2</math> ounces out of the <math>14</math> ounces of liquid, she drank |
<math>\frac{2}{14}=\frac{1}{7}</math>th of the cream. So there is <math>2\cdot\frac{6}{7}=\frac{12}{7}</math> ounces of cream left. | <math>\frac{2}{14}=\frac{1}{7}</math>th of the cream. So there is <math>2\cdot\frac{6}{7}=\frac{12}{7}</math> ounces of cream left. | ||
Revision as of 16:45, 2 June 2021
Problem
Joe and JoAnn each bought 12 ounces of coffee in a 16 ounce cup. Joe drank 2 ounces of his coffee and then added 2 ounces of cream. JoAnn added 2 ounces of cream, stirred the coffee well, and then drank 2 ounces. What is the resulting ratio of the amount of cream in Joe's coffee to that in JoAnn's coffee?
Solution
After drinking and adding cream, Joe's cup has ounces of cream.
After adding cream to her cup, JoAnn's cup had ounces of liquid. By stirring and then drinking
ounces out of the
ounces of liquid, she drank
th of the cream. So there is
ounces of cream left.
So the desired ratio is:
This is problem 6.2.5 in the Art of Problem Solving's
See Also
2006 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.