intermediate algebra

[Gail Price]

can you solve this story problem
By cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base is to be 80 square inches, then what size should be cut from each corner?

 

[Denis]

Gail, I think the 11 inches should be 12 inches...please CHECK!!

 

[mmm4444bot]

What is the area of the sheet of cardboard before it is cut?

\(\displaystyle Area = Length \times Width\)

\(\displaystyle 11 \times 14 = 151\)

The cardboard is 151 square inches.

When the flaps are folded up (I'm assuming that you understand the construction of the box from a flat piece of cardboard), what's leftover for the base is 80 square inches.

We've removed 2x inches from both the width and the length, and the area went from 151 square inches down to 80 square inches.

\(\displaystyle (11 - 2x)(14 - 2x) = 80\)

Solve for x, and report your answer using a complete sentence.

(I got a decimal approximation for x, so I rounded it to the nearest 10th of an inch.)

MY EDIT: Fixed error to show that 2x is subtracted from both dimensions

 

[mmm4444bot]

Gail, I think the 11 inches should be 12 inches...please CHECK!!

Ah, yes. That change would make for Whole numbered solutions for x versus radical expressions. (I'm so impressed with Denis' work here.)

 

[Denis]

Re:

Gail, I think the 11 inches should be 12 inches...please CHECK!!

Ah, yes. That change would make for Whole numbered solutions for x versus radical expressions. (I'm so impressed with Denis' work here.)

Ready to start my Fan Club?

 

[mmm4444bot]

Ready to start my Fan Club?

Did you and your brother-in-law have a final showdown?

 

[Gail Price]

No sir the 11 inches should be 11 inches. Why would you think that it should be 12 inches. That is exactlly how it is wrote.

 

[Mrspi]

can you solve this story problem
By cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base is to be 80 square inches, then what size should be cut from each corner?

If you remove a square of side x inches from EACH corner, and fold up the sides, the base will have a width of 11 - 2x and a length of 14 - 2x.

And the area of the base is to be 80 square inches. So,

(11 - 2x)(14 - 2x) = 80

Solve that for x. If you're still having trouble with this problem, please repost and show ALL of the work you've done to attempt to complete the solution.

 

[Denis]

No sir the 11 inches should be 11 inches. Why would you think that it should be 12 inches. That is exactlly how it is wrote.

This is what you need to solve, as Mrspi showed you:
(11 - 2x)(14 - 2x) = 80
Solving this will NOT give an integer solution for x.
But if 12 instead of 11 is used:
(12 - 2x)(14 - 2x) = 80
then solution will be x = 2, an integer; LOOK:
(12 - 2*2)(14 - 2*2) = (12 - 4)(14 - 4) = (8)(10) = 80

 

[mmm4444bot]

Why would you think that it should be 12 inches[?] That is exactlly how it is [written].

I answered this question, yesterday.

?

Gail, I think the 11 inches should be 12 inches...please CHECK!!

Ah, yes. That change would make for Whole numbered solutions for x versus radical expressions.

In other words, if the given dimension were to be 12 inches, then the answer for x would not need to be a decimal approximation.

Since your instructer did not specify to how many decimal places the answer is to be rounded, Denis conjectured that perhaps the 11-inch value was misstated.

As it is, you need to use the Quadratic Formula to solve for x, and then you need to round it. I suggest that you round the solution for x to the nearest tenth of an inch.

Also, I apologize for posting the wrong set-up. I am glad that Mrs. Pi provided you with the correct factors, and I've edited my first post to correct my error.

What did you get for your answer?