Question 353690
Let x = the larger integer.
Then x-1 would be the next smaller integer.
Now "The larger of two consecutive integers is 11 more than one half the smaller." translates into:
{{{x = 11 + (1/2)(x-1)}}}
Simplifying we get:
{{{x = 11 + (1/2)x-1/2)}}}
Get rid of the fractions by multiplying both sides by 2:
{{{2x = 22 + x - 1}}}
{{{2x = 21 + x}}}
Subtracting x from each side we get:
{{{x = 21}}}
"x", as we said earlier, is the larger integer and "x-1" or 20 is the smaller integer. To check you can easily determine that the larger number, 21, is actually 11 more than half of the smaller, 20.