SOLUTION: Trying to figure out the equation for the following word problem: A carpenter is building a shelving system and cuts a 14-foot long of cherry, shelving into three pieces. The seco

Algebra ->  Linear-equations -> SOLUTION: Trying to figure out the equation for the following word problem: A carpenter is building a shelving system and cuts a 14-foot long of cherry, shelving into three pieces. The seco      Log On


   

Question 1065917: Trying to figure out the equation for the following word problem:
A carpenter is building a shelving system and cuts a 14-foot long of cherry, shelving into three pieces. The second piece is twice as long as the first, and the third piece is 2 feet longer than the first. Find the length of each piece of cherry shelving.
Help is greatly appreciated.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= length (in feet) of the first piece of shelving
2x= length (in feet) of the second piece of shelving
x%2B2= length (in feet) of the third piece of shelving
That should add the the 14 feet length of shelving the carpenter cut,
so x%2B2x%2Bx%2B2=14 is the equation to start with.
Of course, it can be "simplified" by "collecting like terms" to
4x%2B2=14 .
Solving that, you get
4x%2B2=14
4x=14-2
4x=12
x=12%2F4
highlight%28x=3%29
and then 2x=2%2A3.=6
and x%2B2=3%2B2=5 .
So, the first, second and third pieces of shelving are
3 feet long, 6 feet long, and 5 feet long respectively.