Question 558218: The carpenter saws a board that is 22 feet long into two pieces. One piece is to be 1 foot longer than twice the length of the shorter piece. Find the Length of each piece.
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! I just noticed that you are solving this with a System of Equations, which means that you want to solve two equations and two unknowns:
The sum of the pieces is 22 feet, so x+y=22
The larger piece is 1 more than twice the shorter piece, so y=2x+1.
You have to solve this:
x+y=22
y=2x+1
Solve by substitution:
x+(2x+1)= 22
The rest of the solution is as it is solved below. My reference on this type of solution on my own website is in Basic Algebra, Chapter 4, Section 4.08 Applications of Systems of Equations. The Solutions to my exercises are in COLOR!!
If you want to solve this in only one variable:
Let x= shorter piece
2x+1= longer piece
x+2x+1=22
3x+1=22
3x=21
x=7 feet Shorter piece
2x+1=14+1= 15 feet Longer piece
Check: 7 + 15= 22
For additional help with this, please see my own FREE website. To go to my website, use the easy-to-spell and easy-to-remember link www.mathinlivingcolor.com. At the very bottom of this page, there is a link that will take you to my Homepage.
I have a LOT of resources about WORD PROBLEMS on my website. Once you are on my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "Basic Algebra", and look in Chapter 1, Sections 1.09 and 1.10 for a complete, non-traditional explanation that my own students, before I retired, found a lot easier to understand than the published textbooks of that day. You should really like my MATH IN LIVING COLOR pages, where the most difficult problems are solved IN COLOR.
Everything on the website is FREE. If you find something you really like, just print your own copy of it!!
If anyone needs to contact me, especially about the website, my Email address is rapaljer@seminolestate.edu. I'll be glad to help you find an explanation on my website to help you with your algebra topic!
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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