The equations representing the total monthly charges for cell phone plans A and B are y = 50 + 0.20x and y = 45 + 0.30x respectively, where x is the number of messages sent over the initial 500 included in the flat rate, and y is the total monthly charge.
To create the equations for cell phone plans A and B based on the total monthly charges and the number of text messages sent, we can use the provided information to find the cost per additional message over the 500-message flat rate.
For plan A, we know that at 500 messages the charge is $50.00, and for 580 messages the charge is $66.00. The difference in messages is 580 - 500 = 80 messages. The difference in charge for these additional messages is $66.00 - $50.00 = $16.00. Thus, the additional cost per message for plan A is $16.00 / 80 messages = $0.20 per message. The equation for plan A can therefore be written as:
y = 50 + 0.20x, where x is the number of messages over 500, and y is the total monthly charge.
Similarly, for plan B, at 500 messages the charge is $45.00 and at 580 messages it is $69.00. The difference in messages is again 80. The difference in charge for these messages is $69.00 - $45.00 = $24.00, and the additional cost per message for plan B is $24.00 / 80 messages = $0.30 per message. Hence, the equation for plan B can be written as:
y = 45 + 0.30x.
The probable question may be:
"Three cell phone plans, A, B, and C, each have a different flat monthly rate for the first 500 text messages and a different constant rate for every additional message over 500. These tables show the monthly charges for plans A and B when different numbers of messages are sent. Plan A Cell Phone Charges
Number of Messages
Total Month Charge
500
$50.00
580
$66.00
Number of Messages
500
580
Total Month Charge
$50.00
$66.00
Plan B Cell Phone Charges
Number of Messages
Total Monthly Charge
500
$45.00
580
$69.00
Number of Messages
500
580
Total Monthly Charge
$45.00
$69.00
Part A Letting x represent the number of messages over 500, and y the total monthly charges, write equations representing the charges for plans A and B. "