At the local dairy farm, Kareem buys a 32-oz container of yogurt for $2.56. Jonah buys a 6-oz container of yogurt for $0.48. Are

Answer:

Yes, the cost in dollars and the quantity of yogurt are indeed proportional.

The relationship can be expressed as:

Step-by-step explanation:

1. If varies directly with , it can be represented as:

Here, represents the constant of proportionality.

2. We'll calculate the proportionality constant. Given that and , we have:

3. Thus, the equation becomes:

4. Now, we need to verify proportionality. Substituting , which is the quantity of yogurt purchased by Jonah, we should arrive at $0.48:

5. They are indeed directly proportional.

Answer:

Yes, the cost, y, in dollars and the quantity of yogurt, x, are in proportion.

X is directly related to y.

Step-by-step explanation:

Given data:

X1 = 32-oz

y1 = $2.56

x2 = 6-oz

y2 = $0.48

Prove x ∝ y

Solution:

Assume that x ∝ y

Thus,             x = k.y

                  k = x/y

Now, K denotes the constant of proportionality, which can be determined by substituting the values of x1 and y1 into the above equation:

k = 32-oz/$2.56 = 12.5

Proportionality constant = 12.5

Explanation of x ∝ y:

x is directly tied to y. To elucidate this, we can substitute the value of y2 and k into the equation. If the computed value of x matches the given value, then x is proportionate to y.

Equation: x = k.y

x = 12.5 × 0.48 = 6

x = x2(6-oz)

This matches x2.

Hence, it is established that x ∝ y.