1993 UNCO Math Contest II Problems/Problem 3
Problem
A student thinks of four numbers. She adds them in pairs to get the six sums
What are the four numbers? There are two different solutions.
Solution
Let the numbers be ,
,
, and
. Writing in terms of these, we have:
.
Adding these up, we have , so
. Adding the first two equations, we get
. Subtracting this, we obtain
. Adding to the third equation, we have
, so
. Substituting, we have
.
, and
as one of our solutions.
- second solution needed
See also
1993 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
All UNCO Math Contest Problems and Solutions |