Question

Task #1: Comparing Phone Plans Plus telecommunications offers a plan of $20 per month for an unlimited calling and data plan and 10 cents per text message sent. TalkMore, a competing company, offers a plan of $55.00 per month for an identical unlimited calling and data plan and five cents per text message. How can you determine which plan will be cheaper for you?

Answer 1

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).