The table shows the proportional relationship between the number of uniform shirts for a soccer team and the cost.
Number of Uniform Shirts Cost (in dollars)
9 148.50
15 247.50
21 346.50
Determine the constant of proportionality.
99.50
54
16.50
6
To determine the constant of proportionality, we can look at the relationship between the number of uniform shirts and the cost. We can calculate the ratio of the cost to the number of uniform shirts for each set of data points.
For the first set of data points (9 uniform shirts and $148.50), the ratio is 148.50/9 = 16.50.
For the second set of data points (15 uniform shirts and $247.50), the ratio is 247.50/15 = 16.50.
For the third set of data points (21 uniform shirts and $346.50), the ratio is 346.50/21 = 16.50.
Since the ratio is the same for all three sets of data, the constant of proportionality is 16.50.
Therefore, the correct answer is 16.50.
To determine the constant of proportionality, you can choose any two sets of values from the table and calculate the ratio between the number of uniform shirts and the cost. Let's choose the first two sets of values:
For the first set:
Number of uniform shirts = 9
Cost = 148.50
The ratio is: 148.50 / 9 = 16.50
For the second set:
Number of uniform shirts = 15
Cost = 247.50
The ratio is: 247.50 / 15 = 16.50
As you can see, the ratio is the same for both sets of values. Therefore, the constant of proportionality is 16.50. So, the correct answer is 16.50.
To determine the constant of proportionality, we need to find the ratio between the number of uniform shirts and the cost for each given set of values.
First, let's calculate the ratio for the first set of values:
9 uniform shirts / 148.50 dollars = 0.0606 (rounded to four decimal places)
Now, let's calculate the ratio for the second set of values:
15 uniform shirts / 247.50 dollars = 0.0606 (rounded to four decimal places)
Lastly, let's calculate the ratio for the third set of values:
21 uniform shirts / 346.50 dollars = 0.0606 (rounded to four decimal places)
Notice that the ratios for all three sets of values are the same, 0.0606.
Therefore, the constant of proportionality is 0.0606, which is equivalent to 6/100 or 6.
So, the correct answer is 6.