1. ## lost

the smaller of two consecutive even integers is six more than half the larger. find the integers

2. Originally Posted by liar
the smaller of two consecutive even integers is six more than half the larger. find the integers
Solve for n:

$2n = \frac{1}{2} (2n + 2) + 6$.

3. Originally Posted by liar
the smaller of two consecutive even integers is six more than half the larger. find the integers
The steps:

i) The integers are two apart (as all evens are, and as all odds are). Pick a variable for the smaller one.

ii) Write an expression for the larger number in terms of the variable in (i).

iii) Write an expression, in terms of (ii), for "half the larger".

iv) Write an expression, in terms of (iii), for "six more than" "half the larger".

v) Write an equation, in terms of (i) and (iv), for "(the smaller) is (six more than half the larger)".

vi) Solve the equation in (v) for the value of the variable.

vii) Back-solve, using (i) and (ii), for the values of the two numbers.

4. Originally Posted by liar
the smaller of two consecutive even integers is six more than half the larger. find the integers
smaller even integer $= x$
larger even integer $= x+2$

$\frac{1}{2}(x+2)+6=x$
$\frac{1}{2}x+7=x$
$x=14$ (smaller even integer)
$x+2=16$ (larger even integer)