Question

Dylan has a fish tank at home. He knows its height, h, is one inch less than twice the width, w, and the length, l, of the fish tank is seven inches longer than the height.
Which of the following statements is true?

The trinomial expression 4w3 - 10w2 + 6w represents the volume of the fish tank.
The binomial expression 4w3 + 10w2 represents the volume of the fish tank.
The monomial expression 2w represents the height of the fish tank.
The binomial expression 2w + 6 represents the length of the fish tank.

Answer 1

I don't know if I'm right but I think the 4th one (The binomial expression 2w+6 represents the length of the fish tank). Again, I'm not 100% sure if I'm right but from reading the information given, I found this one to be true.

Answer 2

The right answer is: The binomial expression 2w + 6 represents the length of the fish tank.

Dylan has a fish tank, so we assume that this tank is a cube. In this way, the volume of the tank is given by this expression:

$V = w.h.l$

Where:

h: height

w: width

l: length

We know the following things:

FIRST. He knows its height, h, is one inch less than twice the width, w.

This can be expressed as the following equation:

$h=2w-1$

SECOND. The length, l, of the fish tank is seven inches longer than the height.

We can express this statement as follows:

$l=h+7 \\ \\ \therefore l=2w-1+7 \\ \\ \therefore l=2w+6$

By substituting $h \ and \ l$ in $V$:

$V=w.h.l \\ \\ \therefore V=w(2w-1)(2w+6) \\ \\ \therefore V=w(4w^2-12w-2w-6) \\ \\ \therefore \boxed{V=4w^3-14w^2-6w}$