Dimensions of a cereal box

Question

The volume of a 10-oz box of corn flakes is 180.4in³. The width of the box is 3.2 inches less than the length, and its depth is 2.3 inches. Find the length and the width of the box

Answer 1

We know that the volume of the box is width times depth times length, so we need to use the information from this scenario to create a variable & determine the missing measurements. Then you will end up with a quadratic equation, which you can either factor or use the quadratic formula to find the solution.

 

One of the unknown measurements - width - is dependent upon the other unknown measurement - length - so let's set an independent variable: length=x.

 

If length is equal to x, then width must be x-3.2 inches, so you now know all the measurements:

 

x inches=length

x-3.2 inches= width

2.3 inches= depth

 

The quotient of these measurements equals the volume of the box: (x)(x-3.2)(2.3) = 180.4 in³

 

I suggest dividing each side by 2.3 inches, in order to save yourself a step or two: x²-3.2x inches² = 78.435 inches²

 

Subtract 78.435 in² from each side: x²-3.2x-78.435 = 0

 

Factoring this is not very easy, but it is possible: (x+7.3997)(x-10.5997)=0

 

Do you know what to do now? There are two solutions for x, but one of them is negative. Since the box length cannot be negative, the negative solution must be discarded. The positive measurement is the correct one.

 

Finally, use the length to find the measurement of the width. I believe you will find that it equals the absolute value of the negative solution - interesting how that works out!