Difference between revisions of "2006 AMC 12B Problems/Problem 14"
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== Problem == | == Problem == | ||
Elmo makes <math>N</math> sandwiches for a fundraiser. For each sandwich he uses <math>B</math> globs of peanut butter at <math>4</math> cents per glob and <math>J</math> blobs of jam at <math>5</math> cents per glob. The cost of the peanut butter and jam to make all the sandwiches is <math>\</math><math> 2.53</math>. Assume that <math>B</math>, <math>J</math> and <math>N</math> are all positive integers with <math>N>1</math>. What is the cost of the jam Elmo uses to make the sandwiches? | Elmo makes <math>N</math> sandwiches for a fundraiser. For each sandwich he uses <math>B</math> globs of peanut butter at <math>4</math> cents per glob and <math>J</math> blobs of jam at <math>5</math> cents per glob. The cost of the peanut butter and jam to make all the sandwiches is <math>\</math><math> 2.53</math>. Assume that <math>B</math>, <math>J</math> and <math>N</math> are all positive integers with <math>N>1</math>. What is the cost of the jam Elmo uses to make the sandwiches? |
Revision as of 16:03, 22 February 2009
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 |