Claudia works as a manufacturer of decorative jewelry boxes. A customer would like her to create some boxes with the following conditions:
1.The sum of the length and width must be 30 centimeters..
2.The height must be 3 centimeters less than the length..
3.The box should have the greatest possible volume..
Let's do some math to see if we can decide what size boxes Claudia needs to make, and show what we know about polynomials in the process. Remember: One formula we can use to find the volume of a box is v=lwh.

If the length of the box is x, write an expression for the width in terms of x.

Question

Claudia works as a manufacturer of decorative jewelry boxes. A customer would like her to create some boxes with the following conditions: 
1.The sum of the length and width must be 30 centimeters..
2.The height must be 3 centimeters less than the length..
3.The box should have the greatest possible volume.. 
Let's do some math to see if we can decide what size boxes Claudia needs to make, and show what we know about polynomials in the process. Remember: One formula we can use to find the volume of a box is v=lwh.

If the length of the box is x, write an expression for the width in terms of x.

anonymous · Answer

$$l+w=30$$$$h=l-3$$ $$V=l*w*h=l*(30-l)*(l-3) = 33l^2-l^3-33l$$
Solve for l. Reply if you don't have a calculator available for that.

anonymous · Answer

I should also mention that your l value can't be >= to 30 (w can't be negative), l must be > 3 (h can't be negative), and neither l nor V(l) can be negative.

anonymous · Answer

If the length of the box is x, write an expression for the height in terms of x.

anonymous · Answer

$$h=l-3, l=x$$
$$h=x-3$$