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Question 944250: Plan A allows 450 minutes for $39.99 with .25/minute for each minute over 450.
Plan B allows 900 minutes for $59.99 with .30/minute for each minute over 900.
Plan C allows 1500 minutes for $99.99 with .35/minute for each minute over 1500.
An equation or inequality to represent each plan above.
Determine for how many minutes each plan is the best option for two customers. Customer Smith uses roughly 750 minutes per month. Customer Jones uses roughly 1350 minutes per month.
I have no idea how to even begin this.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
plan A is 39.99 per month plus .25 * x over 450
plan B is 59.99 per month plus .30 * x over 900.
plan C is 99.99 per month + .35 * x over 1500.
These look like split functions or what are otherwise called piecewise defined functions.
for Plan A, the function would be:
y = 39.99 for 0 <= x <= 450
y = 39.99 + .25 * (x - 450) for x > 450
for Plan B, the function would be:
y = 59.99 for 0 <= x <= 900
y = 59.99 + .30 * (x - 900) for x > 900
For plan C, the function would be:
y = 99.99 for 0 <= x <= 1500
y = 99.99 + .35 * (x - 1500) for x > 1500
Smith uses 750 minutes per month.
Jones uses 1350 minutes per month.
you would analyze each plan at 750 minutes per month for Smith.
you would analyze each plan at 1350 minutes per month for Jones.
For Smith who uses 750 minutes per month:
Plan A costs 39.99 + .25 * (750 - 450) = 39.99 + .25 * 300 = 114.99
Plan B costs 59.99
Plan C costs 99.99
cheapest plan for Smith is plan B.
For Jones who uses 1350 minutes per month:
Plan A costs 39.99 + .25 * (1350 - 450) = 39.99 + .25 * 900 = 264.99
Plan B costs 59.99 + .30 * (1350 - 900) = 59.99 + .30 * 450 = 217.49
Plan C costs 99.99
cheapest plan for Jones is plan C.
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