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 of bananas

Answer 1

To determine the constant of proportionality (k) for each scenario, we need to analyze the input (quantity) and output (cost, number of items, etc.) for each case.

1. **Gallons of gas**: If we have a table showing the gallons of gas and their cost, we would calculate k by dividing the cost by the number of gallons. For example:

Let's say the table shows:
- 1 gallon = $3.00
- 2 gallons = $6.00
- 3 gallons = $9.00

Here, we can calculate k:
- For 1 gallon: k = 3.00 / 1 = $3.00
- For 2 gallons: k = 6.00 / 2 = $3.00
- For 3 gallons: k = 9.00 / 3 = $3.00

Thus, k = $3.00 per gallon of gas.

2. **Candy Bars Sold**: If there's a relationship between the number of candy bars sold and the total earnings, we can analyze it similarly. For instance:

Let's say the table shows:
- 1 candy bar = $1.50
- 2 candy bars = $3.00
- 3 candy bars = $4.50

Here we would calculate k:
- For 1 candy bar: k = 1.50/1 = $1.50
- For 2 candy bars: k = 3.00/2 = $1.50
- For 3 candy bars: k = 4.50/3 = $1.50

Thus, k = $1.50 per candy bar sold.

3. **Eggs per batch of sugar cookies**: If we have a relationship between the number of eggs and the number of batches of cookies, we can calculate k as follows:

Let's assume we have:
- 2 eggs = 1 batch of cookies
- 4 eggs = 2 batches of cookies
- 6 eggs = 3 batches of cookies

Here k = eggs/batch, or:
- For 1 batch: k = 2 eggs / 1 batch = 2
- For 2 batches: k = 4 eggs / 2 batches = 2
- For 3 batches: k = 6 eggs / 3 batches = 2

Thus, k = 2 eggs per batch of sugar cookies.

4. **Pound of Bananas**: Similar calculations could apply. Assume the following data:
- 1 pound of bananas = $1.20
- 2 pounds of bananas = $2.40
- 3 pounds of bananas = $3.60

We can calculate k as follows:
- For 1 pound: k = 1.20 / 1 = $1.20
- For 2 pounds: k = 2.40 / 2 = $1.20
- For 3 pounds: k = 3.60 / 3 = $1.20

Thus, k = $1.20 per pound of bananas.

Now, summarizing:

- **k for gallons of gas** = $3.00
- **k for candy bars sold** = $1.50
- **k for eggs per batch of sugar cookies** = 2 eggs
- **k for pound of bananas** = $1.20