A cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of s

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1 year ago

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A cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of s

coops 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 6 scoops of mix, one and one-half gallons of water are needed.
Part A: Find the constant of proportionality. Show every step of your work. (4 points)

Part B: Write an equation that represents the relationship. Show every step of your work. (2 points)

Part C: Describe how you would graph the relationship. Use complete sentences. (4 points)

Part D: How many gallons of water are needed for 10 scoops of drink mix? (2 points)

please help asap its almost to late

Mathematics

1 answer:

Vitek1552 [10] · Answer 1 · 2024-06-03T02:17:46+03:00

All the answers to the given parts are mentioned below -

<h3>What is the general equation of a Straight line? How it represents a proportional relationship?</h3>

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

m = y/x

OR

y₁/x₁ = y₂/x₂

We have 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 6 scoops of mix, one and one-half gallons of water are needed.

We can write the proportional relationship as -

y = kx

Now, from the given information, we can write -

2 scoops need 0.5 gallon of water

6 scoops need 1.5 gallon of water

So -

k = 2/0.5

k = 2/(1/2)

k = 2 x 2 = 4

Equations that represents the relationship can be written as -

y = 4x + c

Now, 2 scoops need 0.5 gallon of water.