SOLUTION: Hi! I have a word problem for college algebra course and I'm not quite sure how to begin it. The problem says: A rectangle is 30 feet longer than it is wide. If its length were

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Question 1127028: Hi!
I have a word problem for college algebra course and I'm not quite sure how to begin it. The problem says:
A rectangle is 30 feet longer than it is wide. If its length were increased by 50 ft and its width were diminished by 8 feet, its area would be increased by 200 square feet. Find its dimensions.
Thank you so much!
-Maddie

Found 3 solutions by Boreal, greenestamps, ikleyn:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website!
width=x
length=x+30
x+80 (length + 50)
x-8 (width -8)
area is increased by 200 ft^2
initial area is x(x+30) or x^2+30x
final area is (x+80)(x-8)=x^2+72x-640
add 200 to initial area and have final area
so x^2+30x+200=x^2+72x-640
-42x=-840
x=20 feet width
x+30=50 feet length, area is 1000 ft^2
length is increased to 100
width is decreased to 12
area is 1200 ft^2,

Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!

Same solution, basically, as the other tutor... but presented (I hope) so that the algebra is more clear....

The width is x; the length is x+30.

"If the length were increased by 50 and the width decreased by 8 (making the dimensions x-8 and x+80), the area would be 200 greater than originally"

Algebraic translation:

The width is x = 20 feet; the length is x+30 = 50 feet.

CHECK:
20*50 = 1000; (20-8)(50+50) = 12*100 = 1200

Answer by ikleyn(52817)   (Show Source):
You can put this solution on YOUR website!
.
Maddie,

you can find many closely related solved problems on area of rectangles in the lessons
    - Problems on the area and the dimensions of a rectangle
    - Three methods to find the dimensions of a rectangle when its perimeter and the area are given
    - Three methods to find the dimensions of a rectangle when its area and the difference of two dimensions are given
    - Problems on the area and the dimensions of a rectangle surrounded by a strip
    - Cynthia Besch wants to buy a rug for a room
    - Making a box from a piece of cardboard
    - Problems on a circular pool and a walkway around it
    - Had the dimensions of a rectangle be changed . . . (*)
    - OVERVIEW of lessons on dimensions and the area of rectangles and circles and their elements
in this site.

In particular, the lesson (*) of the list contains very similar solved problems.

A convenient point to observe all these lessons and problems (a "top view") is the last lesson of the list ("OVERVIEW").

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic
"Dimensions and the area of rectangles and circles and their elements".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.