Difference between revisions of "2012 AMC 8 Problems/Problem 19"
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Revision as of 15:38, 3 July 2013
Problem
In a jar of red, green, and blue marbles, all but 6 are red marbles, all but 8 are green, and all but 4 are blue. How many marbles are in the jar?
Solution
Let 
be the number of red marbles, 
be the number of green marbles, and 
be the number of blue marbles.
We have three equations:
Now we use some algebraic manipulation.
We add all the equations to obtain a fourth equation:
Now divide by 
on both sides to find the total number of marbles:
. The total number of marbles in the jar is 
.
See Also
| 2012 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 18 |
Followed by Problem 20 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
