Question

2) Jane's phone plan does not allow unlimited texting while overseas. She pays $5.75 for the first 100 textmessages and $0.10 for each additional text thereafter. If Jane plans to spend at most $15.50 on herphone plan, find the greatest number of text messages she can send, excluding the initial 100.

Answer 1

Given the question in the question tab, the following are the solution steps to answer the question

STEP 1: Interpret the statements

`\begin{gathered} \text{Jane paying \$5.75 for the first 100 text means that the pay is constant and is \$5.75} \\ \text{Jane pays additional \$0.10 for each additional text, this means that:} \\ \text{the number of messages will be multiplied by the unit pay of \$0.10 per additional message} \\ \text{Hence, we have the equation below:} \\ 5.75+0.10x=15.50 \\ \text{where x is the number of additional messages that can be sent} \end{gathered}`

STEP 2: Calculate the value of x

`\begin{gathered} 5.75+0.10x=15.50 \\ \text{Collecting like terms:} \\ 0.10x=15.50-5.75=9.75 \\ \text{Divide both sides by 0.10 to get x} \\ (0.10x)/(0.10)=(9.75)/(0.10) \\ x=97.5 \end{gathered}`

Hence, the greatest number of text messages Jane can send, excluding the initial 100 is approximately 97