Question

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.

Answer 1

`x+y=92\\ (1)/(5)x+(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`

Answer 2

x + y = 92

x/5 + y/2 = 34 / both sides *10
10.x/5 + 10.y/2 = 340
2x + 5y = 340
__________________________________

x + y = 92 /both sides *-2
2x + 5y = 340

__________________________________

-2x -2y = -184
+ 2x +5y = 340
3y = 156
y = 32

x + y = 92
x + 32 = 92
x = 60