Difference between revisions of "2002 AMC 12A Problems/Problem 10"
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+ | {{duplicate|[[2002 AMC 12A Problems|2009 AMC 12A #10]] and [[2002 AMC 10A Problems|2009 AMC 10A #17]]}} | ||
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== Problem == | == Problem == | ||
Sarah places four ounces of coffee into an eight-ounce cup and four ounces of cream into a second cup of the same size. She then pours half the coffee from the first cup to the second and, after stirring thoroughly, pours half the liquid in the second cup back to the first. What fraction of the liquid in the first cup is now cream? | Sarah places four ounces of coffee into an eight-ounce cup and four ounces of cream into a second cup of the same size. She then pours half the coffee from the first cup to the second and, after stirring thoroughly, pours half the liquid in the second cup back to the first. What fraction of the liquid in the first cup is now cream? | ||
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== Solution == | == Solution == | ||
− | We | + | We will simulate the process in steps. |
+ | |||
+ | In the beginning, we have: | ||
+ | * <math>4</math> ounces of coffee in cup <math>1</math> | ||
+ | * <math>4</math> ounces of cream in cup <math>2</math> | ||
+ | In the first step we pour <math>4/2=2</math> ounces of coffee from cup <math>1</math> to cup <math>2</math>, getting: | ||
+ | * <math>2</math> ounces of coffee in cup <math>1</math> | ||
+ | * <math>2</math> ounces of coffee and <math>4</math> ounces of cream in cup <math>2</math> | ||
− | + | In the second step we pour <math>2/2=1</math> ounce of coffee and <math>4/2=2</math> ounces of cream from cup <math>2</math> to cup <math>1</math>, getting: | |
+ | * <math>2+1=3</math> ounces of coffee and <math>0+2=2</math> ounces of cream in cup <math>1</math> | ||
+ | * the rest in cup <math>2</math> | ||
− | + | Hence at the end we have <math>3+2=5</math> ounces of liquid in cup <math>1</math>, and out of these <math>2</math> ounces is cream. Thus the answer is <math>\boxed{\text{(D) } \frac 25}</math>. | |
− | + | == See Also == | |
+ | {{AMC12 box|year=2002|ab=A|num-b=9|num-a=11}} | ||
+ | {{AMC10 box|year=2002|ab=A|num-b=16|num-a=18}} | ||
− | + | [[Category:Introductory Algebra Problems]] |
Revision as of 08:04, 18 February 2009
- The following problem is from both the 2009 AMC 12A #10 and 2009 AMC 10A #17, so both problems redirect to this page.
Problem
Sarah places four ounces of coffee into an eight-ounce cup and four ounces of cream into a second cup of the same size. She then pours half the coffee from the first cup to the second and, after stirring thoroughly, pours half the liquid in the second cup back to the first. What fraction of the liquid in the first cup is now cream?
Solution
We will simulate the process in steps.
In the beginning, we have:
ounces of coffee in cup
ounces of cream in cup
In the first step we pour ounces of coffee from cup
to cup
, getting:
ounces of coffee in cup
ounces of coffee and
ounces of cream in cup
In the second step we pour ounce of coffee and
ounces of cream from cup
to cup
, getting:
ounces of coffee and
ounces of cream in cup
- the rest in cup
Hence at the end we have ounces of liquid in cup
, and out of these
ounces is cream. Thus the answer is
.
See Also
2002 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 9 |
Followed by Problem 11 |
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 12 Problems and Solutions |
2002 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
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 |