2006 AMC 12B Problems/Problem 14
Problem
Elmo makes sandwiches for a fundraiser. For each sandwich he uses globs of peanut butter at cents per glob and blobs of jam at cents per glob. The cost of the peanut butter and jam to make all the sandwiches is . Assume that , and are all positive integers with . What is the cost of the jam Elmo uses to make the sandwiches?
Solution
From the given, we know that
(The numbers are in cents)
since , and since is an integer, then or . It is easily deduced that is impossible to make with and integers, so and . Then, it can be guessed and checked quite simply that if and , then . The problem asks for the total cost of jam, or cents, or
See also
2006 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 13 |
Followed by Problem 15 |
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 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.