Difference between revisions of "2019 AMC 8 Problems/Problem 11"
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==Problem 11== | ==Problem 11== | ||
| − | The eighth grade class at Lincoln Middle School has <math>93</math> students. Each student takes a math class or a foreign language class or both. There are <math>70</math> | + | The eighth grade class at Lincoln Middle School has <math>93</math> students. Each student takes a math class or a foreign language class or both. There are <math>70</math> eighth graders taking a math class, and there are <math>54</math> eight graders taking a foreign language class. How many eighth graders take ''only'' a math class and ''not'' a foreign language class? |
<math>\textbf{(A) }16\qquad\textbf{(B) }23\qquad\textbf{(C) }31\qquad\textbf{(D) }39\qquad\textbf{(E) }70</math> | <math>\textbf{(A) }16\qquad\textbf{(B) }23\qquad\textbf{(C) }31\qquad\textbf{(D) }39\qquad\textbf{(E) }70</math> | ||
Revision as of 13:00, 21 November 2019
Problem 11
The eighth grade class at Lincoln Middle School has 
students. Each student takes a math class or a foreign language class or both. There are 
eighth graders taking a math class, and there are 
eight graders taking a foreign language class. How many eighth graders take only a math class and not a foreign language class?
Solution 1
Let 
be the number of students taking both a math and a foreign language class.
By P-I-E, we get 
= .
Solving gives us 
.
But we want the number of students taking only a math class.
Which is 
.
~phoenixfire
See Also
| 2019 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
