2011 AMC 12A Problems/Problem 7
Problem
A majority of the students in Ms. Demeanor's class bought pencils at the school bookstore. Each of these students bought the same number of pencils, and this number was greater than . The cost of a pencil in cents was greater than the number of pencils each student bought, and the total cost of all the pencils was . What was the cost of a pencil in cents?
Solution
The total cost of the pencils can be found by $\text{#students}*\text{#pencils purchased by each}*\text{price of each pencil}$ (Error compiling LaTeX. ! You can't use `macro parameter character #' in restricted horizontal mode.). As the cost is $$ (Error compiling LaTeX. ! Missing $ inserted.)17.7117711771$, so we have to start from the beginning (although this does give us some indication that we are on the right tack, because MAA doesn't want to make things too easy for us).
Therefore, since$ (Error compiling LaTeX. ! Missing $ inserted.)17717, 11, 23(C)(E)(A)(B)(D)$.
Beginning with$ (Error compiling LaTeX. ! Missing $ inserted.)(A) 71123$. However, the problem states that the price of each pencil must exceed the number of pencils purchased, so we can eliminate this.
Continuing with$ (Error compiling LaTeX. ! Missing $ inserted.)(B) 11237\boxed{B}(E)(A)$, if one wants to make doubly sure.
See also
2011 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 6 |
Followed by Problem 8 |
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 |
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