2002 AMC 10A Problems/Problem 9
Problem
There are 3 numbers A, B, and C, such that , and . What is the average of A, B, and C?
Solution
Notice that we don't need to find what and actually are, just their average. In other words, if we can find , we will be done.
Adding up the equations gives so and the average is . Our answer is .
Solution 2
As there are only 2 equations and 3 variables, just set one of the variables to something convenient, like 0. Setting C as 0, we get A is -2, and B is 11 by substitution. By basic arithmetic the average is 3=>B
-dragoon
Solution 3
Start by isolating and in both of the equations, in order to represent the variables and in terms of A. Ending up with the two equations and , we have to calculate the value of the expression . Plugging in for and for , we add them up and end up with a value of 9. Dividing 9 by 3 to compute the average, we get our answer of .
~Darth_Cadet
See Also
2002 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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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