Any algebra geniuses here?

[Anonymous]

I'm usually pretty good at math, but this problem stumped me! Here it is:

A manufacturer wants to build a rectangular stainless steel tank with a holding capacity of 670 gallons, or about 89.58 cubic feet. The tank's walls will be one half inch think, and about 6.43 cubic feet of steel will be used for the tank. The manufacturer wants the outer dimensions of the tank to be related as follows:

-The width should be 2 feet less than the length.

-The height should be 8 feet more than the length.

What should the outer dimensions of the tank be?

Updates

+1 y

Yep, now we know for sure, there are algebra geniuses on GAG!

[TurbulentDan12]

Here's what I believe the answer is (can't trust me 100% but I'm pretty sure):

So you know the inner volume is 89.58 cubic feet. The outer volume is an additional 6.43 cubic feet. In total this is 96.01 cubic feet but we'll round to 96.

W=L-2

H=L+8

so

(L-2)*(L+8)*L=96

L=4 so

W=2 and

H=12

[pawprint]

Let L denote the length of the tank.

Let W denote the width of the tank, where W = L - 2.

Let H denote the height of the tank, where H = L + 8.

Recall that the volume of the tank is L x W x H.

... You should be able to figure out the rest of the problem from there. :)

[pawprint]

I forgot to mention that the outer volume is the sum of the volume of the tank walls + the inner volume of the tank, i.e. 89.58 + 6.43 = 96 approximately. So, now you can solve this for sure.

[Anonymous]

Dang these GAG users are really smart!