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 10: | Line 9: | ||
==Solution== | ==Solution== | ||
| − | 2x + 3y + 3z = 8 | + | <cmath>2x + 3y + 3z = 8</cmath> |
| − | 3x + 2y + 3z = 808 | + | <cmath>3x + 2y + 3z = 808</cmath> |
| − | 3x + 3y + 2z = 80808 | + | <cmath>3x + 3y + 2z = 80808</cmath> |
The Solution can be found by summing the three equations to get: | The Solution can be found by summing the three equations to get: | ||
| − | 8x + 8y + 8z = 81624 | + | <cmath>8x + 8y + 8z = 81624</cmath> |
| − | then solving for x+y+z, divide by 8 to get: | + | then solving for <math>x+y+z</math>, divide by 8 to get: |
| − | 10,203 | + | <math>\boxed{10,203}</math> |
| − | ==See | + | ==See Also== |
| − | + | {{2008 iTest box|num-b=7|num-a=9}} | |
| + | |||
| + | [[Category:Introductory Algebra Problems]] | ||
Latest revision as of 23:59, 21 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:
,
,
,find 
.
Solution
![\[2x + 3y + 3z = 8\]](http://latex.artofproblemsolving.com/2/a/1/2a14f86976f0006057e446c3f0970f5fb0c4fa07.png)
![\[3x + 2y + 3z = 808\]](http://latex.artofproblemsolving.com/c/c/4/cc486d6b3ecfe373cf272b00718fdd5d6d84e17b.png)
![\[3x + 3y + 2z = 80808\]](http://latex.artofproblemsolving.com/2/8/7/2874a5a8159d631a92530d7647cbdc623b0064b2.png)
The Solution can be found by summing the three equations to get:
![\[8x + 8y + 8z = 81624\]](http://latex.artofproblemsolving.com/0/2/8/028394582fe77a1ff56e5a48a79d11e57b419aee.png)
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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