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.
