Kim is deciding between two cell phone plans. Plan A charges a fixed monthly fee of $100 for 1200 minutes and .25 per minute over 1200. Plan B charges a fixed monthly fee of $55 for 1000 minutes and .33 per minute over 1000. At what point of usage would Kim be indifferent between the two plans?
100 + .25 (x-1200) = 55 + .33(x-1000)
Solve for x.
cant be
gotta be!
yes but how could it be 937.50 minutes when you will pay 100 or 55 dollars either way for 1200 or 1000 minutes. It would need to be over those minutes.
To determine at what point of usage Kim would be indifferent between the two plans, we need to set up an equation comparing the costs of each plan.
Let's assume x represents the number of minutes used.
For Plan A, the cost can be calculated as:
Cost(A) = $100 (fixed monthly fee) + ($0.25 per minute) * (number of minutes over 1200)
For Plan B, the cost can be calculated as:
Cost(B) = $55 (fixed monthly fee) + ($0.33 per minute) * (number of minutes over 1000)
To find the point of indifference, we set the costs of the two plans equal to each other:
$100 + ($0.25 per minute) * (x - 1200) = $55 + ($0.33 per minute) * (x - 1000)
Now, we can solve this equation for x:
$100 + $0.25x - $0.25 * 1200 = $55 + $0.33x - $0.33 * 1000
Simplifying further:
$100 + $0.25x - $0.25 * 1200 = $55 + $0.33x - $0.33 * 1000
$100 + $0.25x - $300 = $55 + $0.33x - $330
$100 + $0.25x - $300 = $55 + $0.33x - $330
$0.25x - $0.33x = $55 - $100 - $330 + $300
-$0.08x = -$75
x = -$75 / -$0.08
x = 937.5
Kim would be indifferent between the two plans at 937.5 minutes of usage.