SOLUTION: i'm learning polynomials and such in class and a question came up in one of my group tests. i asked someone else for help and they showed me how to do it but i don't get how to get

Question 385217: i'm learning polynomials and such in class and a question came up in one of my group tests. i asked someone else for help and they showed me how to do it but i don't get how to get from the equation to the answer.
i do not understand how 2w^2+11w=84 gets to whatever the weird answer was. i do not understand how it is a quadratic equation and how to simplify it...please help and thanks so much.
PS. the problem i had on my group test was this:
The length of a picture is one inch less than twice its width. the frame around the picture has a uniform width of two inches and an area of 96 square inches. what are the dimensions of the picture?
i did the equation like this:
(2w+3)(w+4)=96
which simplified to:
2w^2+11w=84
Found 2 solutions by stanbon, mananth:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
i do not understand how 2w^2+11w=84 gets to whatever the weird answer was. i do not understand how it is a quadratic equation and how to simplify it...please help and thanks so much.
PS. the problem i had on my group test was this:
The length of a picture is one inch less than twice its width. the frame around the picture has a uniform width of two inches and an area of 96 square inches. what are the dimensions of the picture?
i did the equation like this:
(2w+3)(w+4)=96
which simplified to:
2w^2+11w=84
----
It's the frame that has an area of 96 sq. inches, not the entire picture.
----
Cheers,
Stan H.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
The length of a picture is one inch less than twice its width. the frame around the picture has a uniform width of two inches and an area of 96 square inches. what are the dimensions of the picture?
...
width of picture = w
length = 2w-1
...
Area of picture = w(2w-1)
...
uniform width of 2 in.surrounding the picture
so width will be w+4
length = (2w-1)+4=2w+3
..
Area of picture + area frame =(w+4)(2w+3)
...
(Area of picture + area frame)-area of picture= area of frame
..
(w+3)(2w+3)-w(2w-1)=96
2w^2+9w+9-2w^2+w=96
10w+9=96
-9 -9
10w=87
/10
cm the width
Length = 2w-1= 2*8.7-1
Length =17.4-1
Lengthcm
RELATED QUESTIONS
Learning to find Maximum and Minimum Values for Applications of Quadratic Functions in my (answered by Podrius)
I think I have the answer to this but not sure how to write it out. Ace Hardware sells... (answered by solver91311)
Hey, I have question about finding a equation for a parabola with a focus of (3,4) and a... (answered by scott8148)
In my college class right now we are learning about polynomials, trinomials, and so on. I (answered by jim_thompson5910)
Is it D? I want to check my answer. A teacher asked students in his class if they had... (answered by ikleyn)
Okay this is Very confusing to me since I just opened my Algebra book for my online class (answered by richard1234)
I hope you can help me.. I am learning algebra, however my teacher gave us this problem... (answered by jim_thompson5910)
Find the slope of the line containing the points (2,7) and (-1,-8). I am completely... (answered by ankor@dixie-net.com,Edwin McCravy)
I just turned 16, and I've been on a homeschooling program for about a year and a half... (answered by mananth)