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 = 92
x/5 + y/2 = 34 / both sides 10
10.x/5 + 10.y/2 = 340
2x + 5y = 340
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x + y = 92 /both sides -2
2x + 5y = 340
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-2x -2y = -184
+ 2x +5y = 340
3y = 156
y = 32
x + y = 92
x + 32 = 92
x = 60
\(x+y=92\\ \frac{1}{5}x+\frac{1}{2}y=34\\\\ x=92-y\\ 2x+5y=340\\\\ 2(92-y)+5y=340\\\ 184-2y+5y=340\\ 3y=156\\ y=52\\\\ x+52=92\\ x=40\)