2008 AMC 12A Problems/Problem 14: Difference between revisions
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What is the area of the region defined by the [[inequality]] <math>|3x-18|+|2y+7|\le3</math>? | What is the area of the region defined by the [[inequality]] <math>|3x-18|+|2y+7|\le3</math>? | ||
<math>\mathrm{(A)}\ 3\qquad\mathrm{(B)}\ \frac {7}{2}\qquad\mathrm{(C)}\ 4\qquad\mathrm{(D)}\ \frac{9}{2}\qquad\mathrm{(E)}\ 5</math> | <math>\mathrm{(A)}\ 3\qquad\mathrm{(B)}\ \frac{7}{2}\qquad\mathrm{(C)}\ 4\qquad\mathrm{(D)}\ \frac{9}{2}\qquad\mathrm{(E)}\ 5</math> | ||
== Solution == | == Solution == | ||
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[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
[[Category:Introductory Geometry Problems]] | [[Category:Introductory Geometry Problems]] | ||
{{MAA Notice}} | |||
Latest revision as of 09:28, 13 March 2016
Problem
What is the area of the region defined by the inequality 
?
Solution
Area is invariant under translation, so after translating left 
and up 
units, we have the inequality
![\[|3x| + |2y|\leq 3\]](http://latex.artofproblemsolving.com/a/1/9/a19f2f8dd7ca0806a76ba3bfc99a47c9ab449dbb.png)
which forms a diamond centered at the origin and vertices at 
. Thus the diagonals are of length 
and 
. Using the formula 
, the answer is 
.
See also
| 2008 AMC 12A (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 | |
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