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) 27 45 72
Amount of Diet Pepsi (oz) 3 5 8

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

1. Unit Rate =
`9mg/oz`

2.
`y = 9x`

Explanation:

Given

Let the amount of caffeine be represented by y

Let the amount of diet pepsi be represented by x;

y: 27 45 72

x: 3 5 8

Calculating the unit rate

The unit rate or constant of proportionality is calculated as thus

`y = rx`

Where y and x are corresponding values of caffeine and pepsi; and r represents the unit rate;

Divide both sides by x

`(y)/(x) = (rx)/(x)`

`(y)/(x) = r`

`r = (y)/(x)`

When y = 27, x = 3

`r = (27)/(3)`

`r = 9 mg/oz`

When y = 45, x = 5

`r = (45)/(5)`

`r = 9 mg/oz`

When y = 72, x = 8

`r = (72)/(8)`

`r = 9 mg/oz`

Notice that the value of r remains constant all through;

Hence, the unit rate is
`9mg/oz`

Equation to represent the proportional relationship

This is defined as follows;

`y = rx` where

y represents tha amount of caffeine and x represents the amount of diet.

r represents the unit rate

Substitute 9 for r in the above equation

`y = rx` becomes

`y = 9x`

This equation represents the proportional relationship