Difference between revisions of "2012 AMC 10A Problems/Problem 8"
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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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Therefore, our numbers are 12, 7, and 5. The middle number is <math>\boxed{\textbf{(D)}\ 7}</math> | Therefore, our numbers are 12, 7, and 5. The middle number is <math>\boxed{\textbf{(D)}\ 7}</math> | ||
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| + | == See Also == | ||
| + | |||
| + | {{AMC10 box|year=2012|ab=A|num-b=7|num-a=9}} | ||
Revision as of 23:51, 8 February 2012
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 | ||
