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| − | ==Problem 10==
| + | #redirect [[2011 AMC 12A Problems/Problem 7]] |
| − | A majority of the 30 students in Ms. Deameanor's class bought pencils at the school bookstore. Each of these students bought the same number of pencils, and this number was greater than 1. 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 <math>\</math><math>17.71</math>. What was the cost of a pencil in cents?
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| − | <math>\text{(A)}\,7 \qquad\text{(B)}\,11 \qquad\text{(C)}\,17 \qquad\text{(D)}\,23 \qquad\text{(E)}\,77</math>
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| − | == Solution ==
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| − | Let <math>x>15</math> be the number of students at the bookstore, <math>p>1</math> be the number of pencils each student bought, and <math>c>p</math> be the price of one pencil. We see that <math>xcp = 1771 = 7 \cdot 11 \cdot 23</math>. Then we must have <math>x=23, c=11, p=7</math> by the original conditions and the answer is <math>c=\boxed{11 \ \mathbf{(B)}}</math>.
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