Difference between revisions of "2012 AMC 10B Problems/Problem 7"
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== Problem 7 == | == Problem 7 == | ||
Revision as of 00:13, 6 September 2020
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 ![$lcm[3,4]=12$](http://latex.artofproblemsolving.com/1/a/d/1ad88f751508c871c757a7654863e5c575b85f58.png)
, 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 | ||
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