Difference between revisions of "2012 AMC 10B Problems/Problem 7"

(Created page with "== 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...")
 
(Solutions)
Line 7: Line 7:
  
 
== Solutions ==
 
== Solutions ==
x=number of acorns that both animals had.
+
Let <math>x</math> be the number of acorns that both animals had.
 +
 
 +
So by the info in the problem:
  
 
<math>\frac{x}{3}=(\frac{x}{4})+4</math>
 
<math>\frac{x}{3}=(\frac{x}{4})+4</math>
Line 13: Line 15:
 
<math>\boxed{x=48}</math>
 
<math>\boxed{x=48}</math>
  
OR
+
This is answer choice <math>\textbf{(D)}</math>
 
 
<math> \textbf{(D)}</math>
 

Revision as of 11:41, 24 February 2012

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?

$\textbf{(A)}\ 30\qquad\textbf{(B)}\ 36\qquad\textbf{(C)}\ 42\qquad\textbf{(D)}\ 48\qquad\textbf{(E)}\ 54$


Solutions

Let $x$ be the number of acorns that both animals had.

So by the info in the problem:

$\frac{x}{3}=(\frac{x}{4})+4$ $\frac{x}{12}=4$ $\boxed{x=48}$

This is answer choice $\textbf{(D)}$

Invalid username
Login to AoPS