Question

A user is charged P400.00 monthly for a Sun and Text mobile plan which include
500 free texts messages. Messages in excess of 500 is charged P1.00. Represent a
monthly cost for the mobile plan using s(t) where t is the number of messages sent
in a month.​

Answer 1

Given:

• A user is charged $P400.00$ monthly for a mobile plan with $500$ free text messages.
• In excess of $500$ text messages, he is charged $P1.00$ per message.
• The total monthly cost for the user is denoted by "$S$".
• The total number of messages sent in a month is denoted by "$t$".

To find:

To represent the monthly cost of mobile plan in terms of the number of messages.

Answer:

• The monthly cost of text message plan is denoted by "$S$".

• The total number of messages sent in a month is denoted by "$t$".

• Total number of free text messages = $500$
• Cost of those first $500$ free text messages = $P400.00$
• It is given that, the messages in excess of $500$ are charged $P1.00$ per message.
• Now, from the given data, considering the value of total text messages "$t$" greater than 500, the number of extra messages is "$t-500$".
• The cost of extra messages (excess of 500) is given by:

$=(t-500)*1.00\\=t-500$

• Now, the total monthly cost of "$t$" text messages can be represented as follows:

$s(t)=400+t-500\\s(t)=t-100$

Final Answer:

The final equation for the representation of monthly cost of "$t$" text messages is $s(t)=t-100$.