Problem:
Determine 3x4​+2x5​ if x1​,x2​,x3​,x4​ and x5​ satisfy the system of equations given below:
2x1​+x2​+x3​+x4​+x5​x1​+2x2​+x3​+x4​+x5​x1​+x2​+2x3​+x4​+x5​x1​+x2​+x3​+2x4​+x5​x1​+x2​+x3​+x4​+2x5​​=6=12=24=48=96​
Solution:
Adding the five given equations, and then dividing both sides of the resulting equation by 6, yields
x1​+x2​+x3​+x4​+x5​=31(1)
Subtracting (1) from the given fourth and fifth equations, we find that x4​=17 and x5​=65. Consequently, 3x4​+2x5​=51+130=181​.
The problems on this page are the property of the MAA's American Mathematics Competitions