$w=3.1+\frac{l}{2}$ $\newline$ The weight, $w$ , in ounces, of a glass soda bottle design with a side length of $l$ inches is given by the equation. By how many ounces does the weight of the bottle increase for every inch of increase in the side length? $\newline$ Choose $1$ answer: $\newline$ (A) $0.5$ $\newline$ (B) $2$ $\newline$ (C) $3.1$ $\newline$ (D) $3.6$

Full solution

w=3.1+\frac{l}{2}

\newline

The weight,

w

, in ounces, of a glass soda bottle design with a side length of

l

inches is given by the equation. By how many ounces does the weight of the bottle increase for every inch of increase in the side length?

\newline

Choose

1

answer:

\newline

(A)

0.5

\newline

(B)

2

\newline

(C)

3.1

\newline

(D)

3.6

Analyze Equation: Analyze the given equation for the weight of the glass soda bottle. $\newline$ The equation is $w = 3.1 + \frac{l}{2}$ . $\newline$ To find out how much the weight increases for every inch increase in side length, we need to look at the coefficient of $l$ in the equation.
Identify Coefficient: Identify the coefficient of $l$ in the equation. $\newline$ The coefficient of $l$ is $\frac{1}{2}$ , which means for every unit increase in $l$ , the weight $w$ increases by $\frac{1}{2}$ .
Convert to Decimal: Convert the coefficient to a decimal or whole number to match the answer choices. $\newline$ $\frac{1}{2}$ as a decimal is $0.5$ .
Match with Answer Choices: Match the result with the given answer choices. $\newline$ The weight of the bottle increases by $0.5$ ounces for every inch of increase in the side length, which corresponds to answer choice (A) $0.5$ .