Difference between revisions of "2006 AMC 10B Problems/Problem 22"
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== See Also == | == See Also == | ||
*[[2006 AMC 10B Problems]] | *[[2006 AMC 10B Problems]] | ||
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+ | *[[2006 AMC 10B Problems/Problem 21|Previous Problem]] | ||
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+ | *[[2006 AMC 10B Problems/Problem 23|Next Problem]] |
Revision as of 15:05, 2 August 2006
Problem
Elmo makes sandwiches for a fundraiser. For each sandwich he uses
globs of peanut butter at
¢ per glob and
blobs of jam at
¢ per blob. The cost of the peanut butter and jam to make all the sandwiches is
. Assume that
,
, and
are positive integers with
. What is the cost of the jam Elmo uses to make the sandwiches?
Solution
The peanut butter and jam for each sandwich costs ¢, so the peanut butter and jam for
sandwiches costs
¢.
Setting this equal to ¢:
The only possible positive integer pairs whose product is
are:
The first pair violates and the third and fourth pair have no positive integer solutions for
and
.
So, and
The only integer solutions for and
are
and
Therefore the cost of the jam Elmo uses to make the sandwiches is ¢ $= $1.65 \Rightarrow D$ (Error compiling LaTeX. Unknown error_msg)