Difference between revisions of "2010 AMC 12B Problems/Problem 3"
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== Problem == | == Problem == | ||
| − | A ticket to a school play cost <math>x</math> dollars, where <math>x</math> is a whole number. A group of 9th graders buys tickets costing a total of | + | A ticket to a school play cost <math>x</math> dollars, where <math>x</math> is a whole number. A group of 9th graders buys tickets costing a total of \$<math>48</math>, and a group of 10th graders buys tickets costing a total of \$<math>64</math>. How many values for <math>x</math> are possible? |
<math>\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 5</math> | <math>\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 5</math> | ||
Revision as of 03:09, 6 September 2021
- The following problem is from both the 2010 AMC 12B #3 and 2010 AMC 10B #8, so both problems redirect to this page.
Contents
Problem
A ticket to a school play cost 
dollars, where is a whole number. A group of 9th graders buys tickets costing a total of $
, and a group of 10th graders buys tickets costing a total of $
. How many values for are possible?
Solution
We find the greatest common factor of and to be 
. The number of factors of is 
which is the answer 
.
Video Solution
https://youtu.be/I3yihAO87CE?t=179
~IceMatrix
See also
| 2010 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 2 |
Followed by Problem 4 |
| 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 | |
| 2010 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 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 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
