Answer:
2000
Step-by-step explanation:
Let [tex]x[/tex] be the total number of text messages sent per month in order for the plans to cost the same each month.
The first cell phone company, The Call, charges $45 per month and $0.24 per text message for the month.
So, the total cost as per the plan of The Call, for x text messages during the month, is
[tex]C_1= 45+0.24x\cdots(i)[/tex]
Another cell phone company, Cellular Plus, charges $65 per month and $0.23 per text message for the month.
So, the total cost as per the plan of Cellular Plus, for x text messages during the month, is
[tex]C_2= 65+0.23x\cdots(ii)[/tex]
As the cost for both the companies are the same, so, compute the number of text messages, x, during the month by equation [tex]C_1[/tex] and [tex]C_2[/tex] from equation (i) and (ii), we have
[tex]C_1=C_2[/tex]
[tex]\Rightarrow 45+0.24x=65+0.23x[/tex]
[tex]\Rightarrow 0.24x - 0.23x=65-45[/tex]
[tex]\Rightarrow 0.01 x = 20[/tex]
[tex]\Rightarrow x = 20/0.01[/tex]
[tex]\Rightarrow x= 2000[/tex]
Hence, there must be 2000 text message to be sent during the month in order to have the same cost from both the companies.