2012 AMC 10B Problems/Problem 7
Contents
Problem 7
For a science project, Sammy observed a chipmunk and a squirrel stashing acorns in holes. The chipmunk hid 3 acorns in each of the holes it dug. The squirrel hid 4 acorns in each of the holes it dug. They each hid the same number of acorns, although the squirrel needed 4 fewer holes. How many acorns did the chipmunk hide?
Solution 1
Let be the number of acorns that both animals had.
So by the info in the problem:
Subtracting from both sides leaves
This is answer choice
Solution 2
Instead of an Algebraic Solution, we can just find a residue in the common multiples of and , so , the next largest is , the next is , and so on, with all of them being multiples of , now we can see that per every common multiple, we can see a pattern such as
so hole less.
so holes less.
so holes less.
so holes less.
So we see that is the number we need which is
See Also
2012 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.