Cristian M. answered • 07/25/22
Researcher and Analyst Offers Patient and Clear Tutoring
Question: Ella is deciding between two cell phone plans:
plan A: $35 plus 5 cents/min
plan B: $65 with unlimited minutes
which plan should she sign up for?
Solution: Turn the plans' billing methods into equations"
Plan A: $35 fixed + $0.05 per minute (depends on the number of minutes, so $0.05 for a minute, $0.10 for two minutes, $0.15 for three minutes, etc.). So use this equation: y = 35 + 0.05x, where x is the number of minutes and y is the billed amount in dollars.
Plan B: $65 fixed (and that's it!). So use the equation y = 65. No matter how many minutes, you're paying $65 per month. Note how there is no x-term here since you're paying $65 no matter how many minutes (represented by x) you're talking for.
Visually, Plan A has an upward-sloping line that starts from (0,35) (because we can't have negative amounts of minutes, so we're focused on quadrant 1 of a coordinate plane), and is below the flat horizontal line represented by y = 65 (the line for Plan B). There will come a time when the two lines touch, and from that point, the y = 65 line will always be below the line for Plan A.
When do the two plans cost the same in a given month? Set the equations equal to each other to find out!
y = 35 + 0.05x
y = 65
Both equations are equal to y, so...
35 + 0.05x = 65
Now solve for x:
0.05x = 30
x = 600
This means that the phone plans cost the same at 600 minutes, or 10 hours. The plans both cost $65 at that point since the lines intersect at (600, 65) on the coordinate plane (600 minutes, $65).
The original problem doesn't say how to decide on a plan, but here's what we know: Plan A is cheaper for the first 600 minutes (or ten hours) of talking/calling. After that, Plan B is cheaper. But then again, do you talk for ten hours each month? Consider your own talking/calling tendencies before making a decision, but objectively, Plan A is cheaper for the first 600 minutes (or 10 hours). I hope this helps!
