Difference between revisions of "2012 AMC 10A Problems/Problem 8"
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+ | {{duplicate|[[2012 AMC 12A Problems|2012 AMC 12A #6]] and [[2012 AMC 10A Problems|2012 AMC 10A #8]]}} | ||
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== Problem == | == Problem == | ||
The sums of three whole numbers taken in pairs are 12, 17, and 19. What is the middle number? | The sums of three whole numbers taken in pairs are 12, 17, and 19. What is the middle number? | ||
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{{AMC10 box|year=2012|ab=A|num-b=7|num-a=9}} | {{AMC10 box|year=2012|ab=A|num-b=7|num-a=9}} | ||
+ | {{AMC12 box|year=2012|ab=A|num-b=5|num-a=7}} |
Revision as of 14:32, 12 February 2012
- The following problem is from both the 2012 AMC 12A #6 and 2012 AMC 10A #8, so both problems redirect to this page.
Problem
The sums of three whole numbers taken in pairs are 12, 17, and 19. What is the middle number?
Solution
Let the three numbers be equal to ,
, and
. We can now write three equations:
Adding these equations together, we get that
and
Substituting the original equations into this one, we find
Therefore, our numbers are 12, 7, and 5. The middle number is
See Also
2012 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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 |
2012 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 5 |
Followed by Problem 7 |
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 |