2014 AMC 10A Problems/Problem 21
Problem
Positive integers and
are such that the graphs of
and
intersect the
-axis at the same point. What is the sum of all possible
-coordinates of these points of intersection?
Solution
Note that intersects the
axis at
, and
intersects the
-axis at
. We are given that the 2 graphs intersect the x-axis at the same point, so
, so
.
The only possible pairs then are
. These pairs give respective
-values of
which have a sum of
.
See Also
2014 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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