SOLUTION: A water tank that has the form of a rectangular prism, in which the quadruple of the width exceeds the length by 8m and its height is the width divided by 4 plus 1m. If the volume

Question 859652: A water tank that has the form of a rectangular prism, in which the quadruple of the width exceeds the length by 8m and its height is the width divided by 4 plus 1m. If the volume of the tank is equal to 64000 liters, find the tank's dimensions.
This is what I have done so far, but I've had no luck afterwards
w = x
l = 4x - 8
h = x/4 + 1
Then I multiplied it since volume is L x W x H, nonetheless I had this big polynomial which I didn't know how to work with.
x^3 - 6x^2 - 8x = 64000
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
x for length
w for width
h for height
-
Description of the numbers exactly into symbols:
-
, units of meters
4w-8-x=0
-x=8-4w
x=4w-8, this will be used for substitution
-
, units of meters
Usable as it is, to be used for substitution
-
LITERS;
The reason for a factor, k, is that we should be certain to convert our into liters; some people will know the factor just by looking, some people will not.

.

, factor k now known
Make the substitutions,

DIVIDE both members by 1000, multiply both members by 4;

, but we can now also divide both members by 4;

Obviously this equation would still need to be solved for w, and then the x and h can be calculated. I'm stopping here, just so you can get comfortable with how that equation was obtained, and see that it is somewhat different than the equation you found. You might try either a graphing calculator or Rational Roots Theorem to get w.
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