Question

The amount of caffeine consumed from a glass of Diet Pepsi is proportional to the number of ounces that was drank. The table below shows the amount of caffeine consumed by three different people and the corresponding number of ounces of Diet Pepsi that they each drank.
Amount of Caffeine (mg) 24 36 48
Amount of Diet Pepsi (oz) 8 12 16
What is the unit rate (or constant of proportionality)?
Write an equation to represent this proportional relationship. Make sure to define the variables you used.

Answer 1

Answer:

Constant of proportionality: $k=3$

Equation: $c=3d$

Step-by-step explanation:

By definition, Direct proportion equations have the following form:

$y=kx$

Where "k" is the Constant of proportionality.

In this case, let be "c"  the the amount of caffeine consumed  (in mg) from a glass of Diet Pepsi and "d" the number of ounces that was drank.

So, the equation that represents this relationship will have this form:

$c=kd$

Then, the first step is to find the Constant of proportionality "k".

Knowing that:

$c=24;d=8$

We can substitute values into the equation:

$24=k(8)$

Now, solving for "k", we get:

$\frac{24}{8}=k\\\\k=3$

Therefore, we can write the following equation that represents that proportional relationship:

$c=3d$