Difference between revisions of "2007 AMC 8 Problems/Problem 1"
(→Solution) |
Quantummech (talk | contribs) (→Solution) |
||
| Line 10: | Line 10: | ||
| − | Let <math>x</math> be the number of hours she must work for the final week. We are looking for the average, so < | + | Let <math>x</math> be the number of hours she must work for the final week. We are looking for the average, so |
| − | + | <cmath>\frac{8 + 11 + 7 + 12 + 10 + x}{6} = 10</cmath> | |
Solving gives: | Solving gives: | ||
| − | + | <cmath>\frac{48 + x}{6} = 10</cmath> | |
| − | < | ||
| − | < | + | <cmath>48 + x = 60</cmath> |
| − | < | + | <cmath>x = 12</cmath> |
So, the answer is <math> \boxed{\textbf{(D)}\ 12} </math> | So, the answer is <math> \boxed{\textbf{(D)}\ 12} </math> | ||
Revision as of 08:20, 27 August 2015
Problem
Theresa's parents have agreed to buy her tickets to see her favorite band if she spends an average of 
hours per week helping around the house for 
weeks. For the first 
weeks she helps around the house for 
, 
, 
, 
and hours. How many hours must she work for the final week to earn the tickets?
Solution
Let 
be the number of hours she must work for the final week. We are looking for the average, so
![\[\frac{8 + 11 + 7 + 12 + 10 + x}{6} = 10\]](http://latex.artofproblemsolving.com/4/5/7/457a1f6e032fdaed73d94270ea967818ce3e6fd8.png)
Solving gives:
![\[\frac{48 + x}{6} = 10\]](http://latex.artofproblemsolving.com/3/0/a/30a8628b16500da9cd381bfecc513d948b887d56.png)
![\[48 + x = 60\]](http://latex.artofproblemsolving.com/4/f/4/4f4e15153e7444b765a0c52ef4902ac9003264e6.png)
![\[x = 12\]](http://latex.artofproblemsolving.com/8/9/4/894d41d4b2af608a93a1b87a8b10fc2097d414ea.png)
So, the answer is 
See Also
| 2007 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by First Problem |
Followed by Problem 2 | |
| 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. 
