Problem:
Determine 3x4+2x5 if x1,x2,x3,x4 and x5 satisfy the system of equations given below:
2x1+x2+x3+x4+x5x1+2x2+x3+x4+x5x1+x2+2x3+x4+x5x1+x2+x3+2x4+x5x1+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