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== | ||
| + | <cmath>2x + 3y + 3z = 8</cmath> | ||
| + | <cmath>3x + 2y + 3z = 808</cmath> | ||
| + | <cmath>3x + 3y + 2z = 80808</cmath> | ||
| − | ==See | + | 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 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 | |
| 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 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 • 51 • 52 • 53 • 54 • 55 • 56 • 57 • 58 • 59 • 60 • 61 • 62 • 63 • 64 • 65 • 66 • 67 • 68 • 69 • 70 • 71 • 72 • 73 • 74 • 75 • 76 • 77 • 78 • 79 • 80 • 81 • 82 • 83 • 84 • 85 • 86 • 87 • 88 • 89 • 90 • 91 • 92 • 93 • 94 • 95 • 96 • 97 • 98 • 99 • 100 | ||
