### Video Transcript

In the following diagram, 𝑏 is the
quantity of water in a full bottle and 𝑔 is that in a full glass. The total quantity of water in the
diagram can be expressed as 𝑏 plus 𝑔 plus 𝑔 plus one-half 𝑏 plus three-fourths
𝑏. Simplify this expression.

In this question, we have been
given an expression for the quantity of water, and we need to simplify it.

We notice in this expression that
there are some like terms, that is, that there are terms with the same variable
raised to the same power. We have 𝑏, one-half 𝑏, and
three-fourths 𝑏, which are all like terms, and the two terms of 𝑔, which are also
like terms. We can rewrite our expression to
move the like terms next to one another and also emphasize that 𝑏 is equal to one
times 𝑏 and 𝑔 is equal to one times 𝑔.

Next, we add together the
coefficients of the like terms. We have one plus one-half plus
three-fourths 𝑏 plus one plus one 𝑔. We must be careful, since we have a
whole number, a half, and fourths in the coefficient of 𝑏. We can convert all of these values
to fourths to make the calculation easier. In terms of fourths, the
coefficient of 𝑏 is four-fourths plus two-fourths plus three-fourths. Simplifying these coefficients, we
have that the expression is equal to nine-fourths 𝑏 plus two 𝑔.

By writing the coefficient of 𝑏 as
a mixed number, we reach our solution, which is that the simplified expression for
the total quantity of water is two and a fourth 𝑏 plus two 𝑔.