Question

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 the cost, y, in dollars and the amount of yogurt, x, proportional? Explain with an equation to represent the relationship.

Answer 1

Answer:

Yes, the cost $y$ in dollars and the amount of yogurt $x$ are proportional.

The equation is: $y=0.08x$

Step-by-step explanation:

1. If $y$ varies directly as $x$, you can write it as following:

$y=kx$

Where $k$ is the constant of proportionality.

2. Let's calculate the value of the constant of proportionality. If $y=2.56$ and $x=32$, you have:

$y=kx\\k=\frac{y}{x}\\k=\frac{2.56}{32}\\k=0.08$

3. Then, the equation is:

$y=0.08x$

4. Let's verify if they are directly proportional. Substitute $x=6$ which is the amount of yogurt bought by Jonah. The result must be $0,48:

$y=0.08(6)\\y=0.48$

5. They are directly proportional.

Answer 2

Answer:

Yes, the cost, y, in dollars and the amount of yogurt, x, proportional.

X is directly proportion 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 Prove x ∝ y

So,             x = k.y

                  k = x/y

Now K is the proportionality constant and its value can be known by putting the values of x1 and y1 in above equation:

k = 32-oz/$2.56 = 12.5

Proportionality constant = 12.5

Explanation of x ∝ y:

x is directly proportional to the y. to explain this lets put the value of y2 and k in equation. if the calculated value of x is equal to given value than the x is directly proportional to y.

Equation: x = k.y

By putting values in equation:

x = 12.5 × 0.48 = 6

x = x2(6-oz)

Which is equal to x2.

Hence proved that x ∝ y.