Question

Mrs. Vasquez purchases 12 gallons of Chick-fil-a Lemonade for $54 for a birthday party. What is the constant of proportionality that relates the cost in dollars, y, to the number of gallons, x?

Please work it out as I don't understand this at all.

Answer 1

The proportionality constant = k = $4.5

Step-by-step explanation:

Given data:

Number of gallons purchase = 12 gallons

Price of gallons purchased = $54

Cost can be described as y, while number of gallons as x

Constant of propotionality = k = ?

Solution:

y ∝ x

= y = kx

= k = y/x

Putting values in above equation:

k = 54/12 =

Proportionality constant = k = $4.5

Step-by-step explanation:

As the number of gallons is increased the money paid to buy them will automatically increased. So its a direct relation. y is directly proportional to x. And the proportionality constant is $4.5.

Answer 2

Answer: k = 4.5 $/gal

Step-by-step explanation:

1) Two variables x and y are in direct proportion when the ratio y / x is constant, i.e. y / x = k.

2) The constant k is named constant of proportionality.

3) Hence, the constant of proportionality can be obtained by determining the quotient y / x for any pair of values.

In this case you have: y = $ 54, and x = 12 gallons of lemoneade, which leads to:

k = y / k = $ 54 / 12 gallons = 4.5 $/gal