Step-by-step explanation:
The minimum charges for the phone service is $35. For, each text message, $0.50 is charged over and above the minimum charges.
This problem can be modeled as a linear equation in the number of text messages sent as follows:[tex]\textrm{Total bill = Minimum charges + (Charge per message)x(Number of messages)}[/tex]
[tex]\textrm{Total Bill = $}35\textrm{ + (Number of messages)x}($0.50)[/tex]
Given that the total bill is $52, number of text messages can be easily computed.
[tex]52\textrm{ = }35+\textrm{(Number of messages)x}0.50[/tex]
[tex]\textrm{(Number of messages)x0.50 = }52-35=7[/tex]
[tex]\textrm{Number of messages = }\frac{7}{0.5}=14[/tex]
∴Number of text messages Juan sent = 14.
