Nadine can send or receive a text message for $0.15 or get an unlimited number for $5.00. Write and solve an inequality to determine how many messages she can send and receive so the unlimited plan is cheaper than paying for each message.
Let's assume Nadine sends and receives x text messages.
According to the given information, the cost of sending or receiving a text message is $0.15, and the cost of an unlimited plan is $5.00.
To find the number of messages for which the unlimited plan is cheaper, we will set up and solve an inequality.
The cost of sending or receiving x messages individually = $0.15x
The cost of the unlimited plan = $5.00
We want the unlimited plan to be cheaper than paying for each message:
$5.00 < $0.15x
Now let's solve for x:
$5.00 < $0.15x
Dividing both sides of the inequality by $0.15:
$5.00/$0.15 < x
33.33... < x
Since the number of messages must be a whole number (you can't send or receive a fraction of a message), the smallest whole number greater than 33.33... is 34.
Therefore, Nadine can send or receive up to 34 messages so that the unlimited plan is cheaper than paying for each message.