The height of a box is 7 inches the length is 3 inches more then the width find the width if the volume is 126

It looks like we have two unknowns here and two possible equations so to solve this we will need to utilize our systems of equations, I will be using the substitution method.

We know that all of the parts multiplied together is equal to the volume.

We know that the volume is 126 square inches

The height is seven inches

The width is unknown, let w be the width

The length is unknown, let l be the length

We know that the length is three inches more than the width (l=w+3)

We know that the height times the length times the width is equal to the volume (7lw=126)

Since we know that l=w+3, we can substitute w+3 in for l,

7 (w+3) (w) = 126

Now we can solve our equation

7 (w+3) (w) = 126

(7w+21) (w)

7w^2+21w=126

Now we will complete the square to solve for w

7w^2+21w=126

w^2+3w=18

w^2+3w+2.25=20.25

(w+1.5) ^2=20.25

w+1.5=4.5

w=3

We have now found out using our knowledge of systems of equations that the width of this prism is 3 inches.