The cost of operating an appliance varies jointly as the number of watts, hours of operation, and the cost per kilowatt-hours. It costs $0.45 to operate a 3000-watt air conditioner for 2 hours at a cost of $0.075 per kilowatt-hour. Find the Cost of operating a 122-watt dishwasher for 40 minutes.
How I calculated: TC (total cost)=k (Watts)(cost)(time) .45=k(3000)(.075)(2) K=.001
Cost=K(watts)(time) Cost=(.001)(1200)(.40)
Cost=.48.......is that correct?
less time and lower wattage ... how can the cost be more?
$0.45 * [(40/60) / 2] * (122 / 3000)
dishwasher is actually 1200 watt (not 122 sorry)...but that is what I thought too which is why I am seeking guidance. thank you for your help....what is the formula you used? when fractions are used doesn't that mean its inverse variation? I thought the problem only said joint variation.
jointly means multiple variables
cost to run dishwasher is the cost to run the ac, multiplied by the ratios of the run time and wattage
... both time and wattage are direct variation
... the ratios are new to old
new cost =
... old cost * (new watts / old watts) * (new time / old time)
To find the cost of operating a 122-watt dishwasher for 40 minutes, we can use the formula:
TC (total cost) = k (watts) * cost * time
Given that TC = 0.45, watts = 3000, cost = 0.075, and time = 2, we can solve for k:
0.45 = k * 3000 * 0.075 * 2
Dividing both sides by 3000 * 0.075 * 2, we get:
k = 0.45 / (3000 * 0.075 * 2)
k = 0.0005
Now, we can substitute the values into the formula to find the cost of operating the dishwasher:
Cost = k * watts * time
Cost = 0.0005 * 122 * (40/60)
Converting 40 minutes to hours (divide by 60), we get:
Cost = 0.0005 * 122 * (2/3)
Cost ≈ 0.04093
Therefore, the cost of operating a 122-watt dishwasher for 40 minutes is approximately $0.04093.