For the following situation determine the independent value of the dependent value in the constant of proportionality for both ratios confirm your calculations by setting up a proportion between the two ratios and cross multiplying reason is a private driver who charges 25.80 or a drive 6 miles in 77.40 to drive 18 miles what is the independent value what is the dependent value what is the constant of proportionality k What is the constant of proportionality K what is the proportion
In this scenario, the independent value is the number of miles driven, and the dependent value is the cost of the drive.
To determine the constant of proportionality (k), we can set up a ratio between the cost and the distance for each given scenario.
For the first scenario:
Cost = $25.80
Distance = 6 miles
Ratio = Cost/Distance
Ratio = $25.80/6 miles
For the second scenario:
Cost = $77.40
Distance = 18 miles
Ratio = Cost/Distance
Ratio = $77.40/18 miles
To find the constant of proportionality, we need to check if the ratio of cost to distance is the same for both scenarios.
Ratio 1 = Ratio 2
$25.80/6 miles = $77.40/18 miles
To solve for k, we just need to cross multiply:
($25.80)(18 miles) = ($77.40)(6 miles)
k = ($25.80)(18 miles) / ($77.40)(6 miles)
k = $46.44 / $464.40
k ≈ 0.10
Therefore, the constant of proportionality (k) is approximately 0.10.
The proportion can be written as:
($25.80/6 miles) = ($77.40/18 miles)