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Question

Question
The constant of proportionality is the amount a relationship will change for each unit.

It is represented by the value of this ratio:

k=yx


One of the ways a proportional relationship is identified is with a table showing the input and output values that change by the same unit rate.

On this table, the pounds of peaches (p) is the input and the cost of the pounds (c) is the output. The constant of proportionality for the table may be determined:

k=yx = 2.251=2.25


All of the ratios on the table are equivalent. 4.52=2.25
6.753=2.25
94=2.25


k = $2.25 per pound of peaches



(4 points)
Determine the constant of proportionality for each table. If the table does not have an constant of proportionality, enter the letter "n" in box.



k = $
per gallon of gas

================================





k = $
per candy bars sold

================================



k =
eggs per batch of sugar cookies

================================



k = $
per pound

Answer 1

To determine the constant of proportionality (k) for each scenario you've described, we need the specific values or tables that correspond to each case. Since those values are not provided here, I can guide you on how to find the constant of proportionality based on a given table of values.

1. For the cost of gas per gallon:

   • To find k, divide the cost (in dollars) by the number of gallons to get the price per gallon.
   • Example: If the table shows 10 gallons cost $30, then k = $30 / 10 = $3 per gallon.

2. For candy bars sold:

   • If you have the number of candy bars sold and their total selling price, you would perform a similar division.
   • Example: If 5 candy bars cost $10, then k = $10 / 5 = $2 per candy bar.

3. For eggs per batch of sugar cookies:

   • Here, we typically look at how many eggs are needed for a certain number of batches of cookies.
   • Example: If a recipe for 3 batches requires 6 eggs, then k = 6 eggs / 3 batches = 2 eggs per batch.

4. For the cost per pound (of a product):

   • Once again, divide the total cost by the total weight in pounds.
   • Example: If 4 pounds cost $8, then k = $8 / 4 = $2 per pound.

Please provide the specific values or tables you mentioned, and I can help compute the exact constants of proportionality for each situation. If you know that there is no constant of proportionality (i.e., the ratios are not equivalent), then simply enter "n."