Question

(Constant of Proportionality, Graphing Proportional Relationships, Real-World Proportional Problems HC)

A restaurant serves pancakes that are made from a powdered pancake mix. There is a proportional relationship between the number of scoops of powdered pancake mix and the amount of water needed to make them. For every 4 scoops of mix, one half quart of water is needed, and for every 12 scoops of mix, one and one half quarts 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 quarts of water are needed for 20 scoops of pancake mix? (2 points)

Answer 1

See below

Explanation:

If I make x the scope of mix and y the quarts of water, my equation would be y = .125x

I can find the constant of Proportionally by y/x

Using points (4,.5) and (12,1.5)

(.5/4) = 0.125

(1.5/12) = 0.125

The equation would then be:

y = 0.125x

C see the graph provided from Desmos (a free graphing calculator). as x Increases by 1, y increases by 0.125

y = 0.125x

y =.0125(20)

y = 2.5

For 20 scoops, I would need 2.5 quarts of water.

You can also see from the graph as 8 scoops, I would need 1 quart of water.