Question 264106
One-fifth of sum of two consecutive integers is 19 less than the smaller integer.
find the smaller of the two integers?
:
Two consecutive integers: x, (x+1)
:
"One-fifth of sum of two consecutive integers is 19 less than the smaller" 
{{{1/5}}}(x + (x+1)) = x - 19
Multiply both sides by 5
2x + 1 = 5x - 95
:
1 + 95 = 5x - 2x
:
96 - 3x
x = {{{96/3}}}
x = 32, the smaller integer
;
:
Check in original equation
{{{1/5}}}(32 + 33) = 32 - 19
{{{1/5}}}(65) = 13