The table below shows the proportional relationship between the weight of yogurt, in ounces, and the number of packs of yogurt: Number of Packs of Yogurt Number of Ounces of Yogurt 2 36 3 54 5 90 What is the constant of proportionality?

In a directly proportional relationship, increasing one variable will increase another. The value of the constant of proportionality is 18 ounces per pack.

What is the directly proportional and inversely proportional relationship?

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

p = kq

where k is some constant number called the constant of proportionality.

This directly proportional relationship between p and q is written as

p∝q where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n be two variables.

Then m and n are said to be inversely proportional to each other if

[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]

(both are equal)

where c is a constant number called the constant of proportionality.

Given that the table shows the proportional relationship between the weight of yogurt, in ounces, and the number of packs of yogurt.

Now, the relation between the weight of yogurt, in ounces, and the number of packs of yogurt can be written as,

Weight ∝ packs

To remove the proportionality the constant of proportionality can be written as,

Weight = k × packs

Substitute values form any one of the rows in the equation,

Weight = k × packs

36 ounces = k × 2 packs

k = 36 ounces / 2 packs

k = 18 ounce per pack

Hence, the value of the constant of proportionality is 18 ounce per pack.

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