x = number of minutes
y = total cost in dollars
For plan A, the equation is
y = 0.20*x + 25
since the cost per min is $0.20 and the monthly fee is $25
Similarly, plan's B cost equation is
y = 0.08*x + 40
When will the two plans cost the same? When they produce the same y value for some given x value.
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To solve, we use substitution
y = 0.20*x + 25
0.08*x + 40 = 0.20*x + 25
0.08*x - 0.20*x = 25 - 40
-0.12x = -15
x = -15/(-0.12)
x = 125
If x = 125, then y is...
y = 0.20*x + 25
y = 0.20*125 + 25
y = 25 + 25
y = 50
The two plans will cost the same when you use 125 minutes. The cost will be $50.
