Question

The sun of three consecutive even integers is 46 more than twice the smallest of the three integers. Find the integers

Answer 1

If "x" is the first even integer, then the second and third are:

$\begin{gathered} y=x+2 \\ z=x+4 \end{gathered}$

Because we need only even integers, so they are separated by 2 units. If their sum is 46 more than twice the smallest one, we can write:

$x+y+z=46+2\cdot x$

Using the two expressions above, we can solve for x.

$\begin{gathered} x+(x+2)+(x+4)=46+2x \\ x+x+2+x+4=46+2x \\ 3x+6=46+2x \\ 3x-2x=46-6 \\ x=40 \end{gathered}$

Therefore the integers are 40, 42 and 44.