The sum of two numbers is 92. One fifth of the first number added to one half of the second number is 34. Find the two numbers.

x + y = 92x/5 + y/2 = 34     / both sides *1010.x/5 + 10.y/2 = 3402x + 5y = 340__________________________________x + y = 92        /both sides *-22x + 5y = 340__________________________________     -2x -2y = -184+    2x +5y = 340                 3y = 156                       y = 32x + y = 92x + 32 = 92x = 60

[tex]x+y=92\\
\frac{1}{5}x+\frac{1}{2}y=34\\\\
x=92-y\\
2x+5y=340\\\\
2(92-y)+5y=340\\\
184-2y+5y=340\\
3y=156\\
y=52\\\\
x+52=92\\
x=40[/tex]