2006 AMC 10B Problems/Problem 22
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?
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 .
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. ! Missing $ inserted.)