Question

A cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of scoops of powdered drink mix and the amount of water needed to make it. For every 2 scoops of mix, one half gallon of water is needed, and for every 5 scoops of mix, one and one fourth gallons of water are needed.
Part A: Find the constant of proportionality. Show every step of your work.

Part B: Write an equation that represents the relationship. Show every step of your work.

Part C: Describe how you would graph the relationship. Use complete sentences.

Part D: How many gallons of water are needed for 12 scoops of drink mix?

Answer 1

Therefore ,the constant of proportionality comes out to be 4 and the equation that represents the relationship is x=1/4y.

What is equation?

Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics. From straightforward algebraic equations that just require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity.

Here,

scoop is represented as x and water is represented as y

therefore, For every 2 scoops of mix, one half gallon of water is needed, and for every 5 scoops of mix, one and one fourth gallons of water are needed.

Equation from the given data is

2x = 1/2y or x=1/4y

and

5x = (1+1/4)y

5x=5/4y

So,

x=1/4y.

Therefore ,the constant of proportionality comes out to be 4

The equation that represents the relationship is x=1/4y.

We can graph the plot by using the given equation x=1/4y

or 4x=y

so for every x value we have to put 4 times its value into y for every point

you point in the graph.

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