Question 709326: Hello, recently I got a word problem from the math teacher which I dont understand how to solve.
The top and the base of a fish tank are rectangles whose length is 10 inches more than the width. If the depth and the width of the tank total 50 inches, and the combined area of the top and the base is 400 in^2 less than the total area of the four sides, What are the dimensions of the tank?
Note: write your answer in the following format,
L= ## W=## D=## where ## is any number.
If you could explain me how to do it, I will appreciate it very much.
Thank you in advance.
Answer by josgarithmetic(39631)   (Show Source):
You can put this solution on YOUR website! As briefly as possible,
L=w+10
d+w=50 (but the description from posted question is not specific enough)
Area of the sides: 
Area of top and base: 
For area of the sides, the process was, 2Ld plus 2dw or 2dL+2dw=2d(L+w).
"the combined area of the top and the base is 400 in^2 less than the total area of the four sides, ", must mean:
 .
First simplification is to divide by 2.
Used next the facts,  and  , substituted and several algebra steps, solving all into terms of L and constants, ...
...
Quadratic formula solution needed to be used. The simple radical form found for L was  or  . The minus-form turned to be a non-useful result.
Length then was  (approximate).
Using the other two facts,  ,  .
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