Answer
both plans have the same cost for \[500\]text messages.
Work Step by Step
Consider the cost of text messages in both the plan as \[x\].
Then, the total cost of the first plan is\[15+0.05(x)\] and the second plan is \[5+0.07(x)\]
As per the problem requires the number of text messages for which the cost for the two plans will be the same.
It means the cost of both the plans must be equal to each other. Then,
\[\begin{align}
& 15+0.05(x)=5+0.07(x) \\
& x(0.05-0.07)=15-5 \\
& x(0.02)=10 \\
& x=500 \\
\end{align}\]
Hence, both plans have the same cost for \[500\]text messages.
