Difference between revisions of "2001 AMC 10 Problems/Problem 22"
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Revision as of 11:11, 4 July 2013
Problem
In the magic square shown, the sums of the numbers in each row, column, and diagonal are the same. Five of these numbers are represented by ,
,
,
, and
. Find
.
Solutions
Solution 1
We know that , so we could find one variable rather than two.
The sum per row is .
Thus .
Since we needed and we know
,
.
Solution 2
The magic sum is determined by the bottom row. .
Solving for :
.
To find our answer, we need to find .
.
See Also
2001 AMC 10 (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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 |
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