Answer:
Let x represents the number of messages and y represents the total cost.
Thus, According to the question,
For, First company,
y = 20 + 0.1 x --------------(1) ( since, 1 cent = 0.1 dollars )
For second company,
y = 55 + 0.05 x ---------------(2)
By solving equations 1) and 2),
We get,
x = 700 and y = 90
Thus, we have three conditions,
Condition 1) For x < 700,
20 + 0.1 x > 55 + 0.05 x
Before 700 messages, the cost of plan (1) is cheaper than plan (2).
Condition 2) For x = 700
20 + 0.1 x = 55 + 0.05 x
⇒ for 700 messages both plan have the equal cost of $ 90.
Condition 3) For x > 700
Since, The slope of line (1) = 0.1 ( after comparing with the general equation of line y = m x +c, where m is the slope of the line)
Similarly, the slope of line (2) = 0.05
Since, 0.05 > 0.1
the slope of line 2) is less than the slope of line 1)
⇒ After 700 messages the cost of plan 2) will be cheaper than that of plan 1).
