How can you find the constant of proportionality for the ratio of price to number of bouquets from the table?
To find the constant of proportionality for the ratio of price to number of bouquets from the table, you need to identify two data points and then use the formula for the constant of proportionality, which is expressed as a ratio.
Let's say the table shows the price and number of bouquets for different types of flowers:
Flower Type | Price | Number of Bouquets
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Roses | $10 | 2
Sunflowers | $15 | 3
Tulips | $20 | 4
To find the constant of proportionality, you can choose any two rows in the table. Let's use the first and second rows.
For the first row (Roses), the price is $10 and the number of bouquets is 2.
For the second row (Sunflowers), the price is $15 and the number of bouquets is 3.
Now, we can calculate the constant of proportionality by dividing the price by the number of bouquets for each row. The resulting values should be the same because we are calculating the constant of proportionality.
For the first row:
Constant of Proportionality = Price / Number of Bouquets = $10 / 2 = $5/1 = $5
For the second row:
Constant of Proportionality = Price / Number of Bouquets = $15 / 3 = $5/1 = $5
Since the constant of proportionality is the same for both rows, we can conclude that the constant of proportionality for the ratio of price to number of bouquets is $5.
A 2-column table with 4 rows. Column 1 is labeled Gallons with entries 2, 4, b, 10. Column 2 is labeled miles with entries 56, a, 168, c.
Alexa is planning to drive across the United States in her car. She started making a table to represent the proportional relationship between gallons of gas and miles driven. The table shows how far she can travel for each gallon of gas that she uses.
What is the constant of proportionality?
miles per gallon
To find the constant of proportionality for the given table, we need to identify two data points that represent the relationship between gallons of gas and miles driven.
Looking at the table, we can see that the relationship between the Gallons and Miles columns is proportional. That means we can find the constant of proportionality by calculating the ratio of miles to gallons for any two data points.
Let's choose two data points from the table - (2, 56) and (10, c).
For the first data point (2, 56), Alexa traveled 56 miles using 2 gallons of gas. The ratio of miles to gallons is:
56 miles / 2 gallons = 28 miles per gallon
For the second data point (10, c), Alexa traveled c miles using 10 gallons of gas. The ratio of miles to gallons is:
c miles / 10 gallons = (c/10) miles per gallon
Since the relationship is proportional, the ratio of miles to gallons should be the same for both data points. Therefore, we can equate the two ratios:
28 miles per gallon = (c/10) miles per gallon
By comparing the ratios, we can determine that the constant of proportionality for the relationship between gallons of gas and miles driven is 28, which means Alexa can travel 28 miles for every gallon of gas she uses.
A 2-column table with 4 rows. Column 1 is labeled Gallons with entries 2, 4, b, 10. Column 2 is labeled miles with entries 56, a, 168, c.
Alexa is planning to drive across the United States in her car. She started filling out the table showing how far she can travel for each gallon of gas that she uses. Find the missing values using the constant of proportionality of 28 miles per gallon.
a =
b =
c =
To find the missing values in the table using the constant of proportionality of 28 miles per gallon, we can utilize the formula for the constant of proportionality, which is the ratio of miles to gallons.
Using the known data points in the table:
For the first data point (2, 56), Alexa traveled 56 miles using 2 gallons of gas. The ratio of miles to gallons is 56 miles / 2 gallons = 28 miles per gallon (using the constant of proportionality).
For the third data point (b, 168), we can solve for b by setting up the equation:
28 miles per gallon = 168 miles / b gallons
To find b, we can cross-multiply and solve for it:
28b = 168
b = 168 / 28
b = 6
Therefore, b equals 6.
For the fourth data point (10, c), we can solve for c using the constant of proportionality of 28 miles per gallon:
28 miles per gallon = c miles / 10 gallons
Again, we can cross-multiply and solve for c:
28 * 10 = c
280 = c
Therefore, c equals 280.
So, the missing values are:
a = 28 (since 28 miles per gallon is the constant of proportionality)
b = 6 (calculated using the constant of proportionality)
c = 280 (calculated using the constant of proportionality)
To find the constant of proportionality for the ratio of price to the number of bouquets, you'll need to use the values from the table. Here are the step-by-step instructions:
Step 1: Locate the table that shows the different prices and the corresponding number of bouquets.
Step 2: Choose any two rows from the table (price_1, bouquets_1) and (price_2, bouquets_2), where price_1 and price_2 represent two different prices, and bouquets_1 and bouquets_2 represent the number of bouquets corresponding to those prices.
Step 3: Calculate the ratio of the price to the number of bouquets for both rows. Divide price_1 by bouquets_1 and price_2 by bouquets_2. This will give you the two ratios.
Step 4: Compare the two ratios obtained in Step 3. If they are equal, then the constant of proportionality exists, and it is equal to the common value of the two ratios.
Step 5: If the two ratios are not equal, repeat Step 2 and Step 3 with different rows until you find two ratios that are equal. Once the equal ratios are found, the constant of proportionality can be calculated as the common value of those ratios.
Note: Ensure that you are choosing rows that have different prices and non-zero number of bouquets to avoid division by zero errors.
To find the constant of proportionality for the ratio of price to the number of bouquets from a table, you need to identify two data points for which the ratio remains the same.
Let's say you have a table with price in one column and the number of bouquets in another column. Choose any two data points, for example, (P1, B1) and (P2, B2), where P1 and P2 are prices and B1 and B2 are the corresponding numbers of bouquets.
Then, calculate the ratio of price to the number of bouquets for both data points:
Ratio1 = P1 / B1
Ratio2 = P2 / B2
If the ratio remains constant, then Ratio1 = Ratio2.
Now, you can solve for the constant of proportionality (k) by setting up the equation:
P1 / B1 = P2 / B2
By cross multiplying, the equation becomes:
P1 * B2 = P2 * B1
Finally, solve for k by dividing both sides of the equation by B1:
k = (P2 * B1) / B2
This value of k represents the constant of proportionality for the ratio of price to the number of bouquets in the given table.