Difference between revisions of "2008 iTest Problems/Problem 8"
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== Problem == | == Problem == | ||
− | |||
− | + | The math team at Jupiter Falls Middle School meets twice a month during the Summer, and the math team coach, Mr. Fischer, prepares some Olympics-themed problems for his students. One of the problems Joshua and Alexis work on boils down to a system of equations: | |
<center><math>2x + 3y + 3z = 8</math>, | <center><math>2x + 3y + 3z = 8</math>, | ||
Line 8: | Line 7: | ||
<math>3x + 3y + 2z = 80808</math>,</center> | <math>3x + 3y + 2z = 80808</math>,</center> | ||
find <math>x+y+z</math>. | find <math>x+y+z</math>. | ||
+ | |||
+ | ==Solution== | ||
+ | <cmath>2x + 3y + 3z = 8</cmath> | ||
+ | <cmath>3x + 2y + 3z = 808</cmath> | ||
+ | <cmath>3x + 3y + 2z = 80808</cmath> | ||
+ | |||
+ | The Solution can be found by summing the three equations to get: | ||
+ | |||
+ | <cmath>8x + 8y + 8z = 81624</cmath> | ||
+ | |||
+ | then solving for <math>x+y+z</math>, divide by 8 to get: | ||
+ | |||
+ | <math>\boxed{10,203}</math> | ||
+ | |||
+ | ==See Also== | ||
+ | {{2008 iTest box|num-b=7|num-a=9}} | ||
+ | |||
+ | [[Category:Introductory Algebra Problems]] |
Latest revision as of 00:59, 22 June 2018
Problem
The math team at Jupiter Falls Middle School meets twice a month during the Summer, and the math team coach, Mr. Fischer, prepares some Olympics-themed problems for his students. One of the problems Joshua and Alexis work on boils down to a system of equations:
![$2x + 3y + 3z = 8$](http://latex.artofproblemsolving.com/b/1/a/b1a949a0479b1c302babf706cac5b421735369c9.png)
,
![$3x + 3y + 2z = 80808$](http://latex.artofproblemsolving.com/5/7/e/57e194550059b7d7a487e6beac99396feca762ea.png)
find .
Solution
The Solution can be found by summing the three equations to get:
then solving for , divide by 8 to get:
See Also
2008 iTest (Problems) | ||
Preceded by: Problem 7 |
Followed by: Problem 9 | |
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