Question

A cereal box has a volume of 441 cubic inches. Its height is 12 inches, its width is x inches, and its length is (x+7) inches. What is the width of the box?

Answer 1

Volume = length * width * height 
441 = (x+7) * x * 12 
All you have to do is just find x which is the width. 

441 = (x+7) * 12x 
441 = 12x2 + 84x 
12x2 + 84x - 441 = 0 

Thus you have a quadratic equation with two possible solution. Use the quadratic formula To calculate the x values. If you calculate it, you will find that x = 3.5 and x = -10.5. To prove which one is the width, substitute these values for x one at a time into the volume equation. Lets take x=3.5 

441 = (x+7)+x+12 
441 = (3.5+7) *3.5*12 
441 = 10.5*3.5*12 
441= 441 

If we try -10.5; 

441 = (x+7) *x*12 
441=(-10.5+7)*10.5*12 
441 = -3.5*10.5*12 
441 = -441 

Therefore clearly, our answer will be x = 3.5... We don't have to use the substitution to prove our answer is 3.5 because logically we can rule out -10.5 inches of width. Realistically, there can never be a negative width. Therefore your width is 3.5 inches. Hopefully this helps!