2008 iTest Problems/Problem 8

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:

$2x + 3y + 3z = 8$,

$3x + 2y + 3z = 808$,

$3x + 3y + 2z = 80808$,

find $x+y+z$.

Solution

\[2x + 3y + 3z = 8\] \[3x + 2y + 3z = 808\] \[3x + 3y + 2z = 80808\]

The Solution can be found by summing the three equations to get:

\[8x + 8y + 8z = 81624\]

then solving for $x+y+z$, divide by 8 to get:

$\boxed{10,203}$

See Also

2008 iTest (Problems)
Preceded by:
Problem 7
Followed by:
Problem 9
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