A piece of lumber which is 55 inches long is cut into two parts such that 2 times the larger part will be 12 more than 5 times the smaller part. How long are each piece?

Let x=the smaller part

Then 55-x=the larger part

Now we are told the following:

2 (55-x) = 5x+12 simplify

110-2x=5x+12 add 2x to and subtract 12 from each side

110-2x+2x-12=5x+2x+12-12 collect like terms

98=7x