word problem

Question

Suppose are building a storage box of volume 4368in³.  The length of the box will be 24in. The height of the box will be 1 in. more than its width. Find the height of the box and width.

Answer 1

Hi Syndey!

 

So we have length * width * height = 4368 in³. If we let width be x in., then the height is (x+1) in. So now,

(x)(x+1)(24) in³=4368 in³. Now we can cancel the in³ and solve for x.

(x)(x+1) = 4368/24

(x)(x+1) = 182

Now we can look for factors of 182 to find the pair where one is just one larger than the other.  But a trick that works every time is the quadratic formula: if we have ax²+bx+c=0, then x=(-b±sqrt(b²-4ac))(2a).  We can get our equation into this form by multiplying out the left side and subtracting 182 from both sides:

x²+x-182=0.  Then the quadratic formula gives 13 and -14. We want x=13 because it doesn't make sense for the width to be negative. So

Solution:

x=13

width: 13 in.

height: 14 in.