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
Let the numbers be , , , and . We have the following 6 equations from the problem statement:
Adding all of these up: gives : call this equation A
Adding first two equations: : call this equation B
Subtracting equation B from A gives us : call this equation C
Adding C to the 4th equation gives
Substituting w in the original equations gives: , ,
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 |