A cell phone provider offers a plan that costs $20 per month plus $0.10 per text message sent or received. A comparable plan costs $40 per month but offers unlimited text messaging. Complete parts a. and b. below.
a. Write an equation to represent the total cost C (in dollars) for sending or receiving t text messages in a month using the first plan.
The equation for the total cost C is given as:
C = $20 + ($0.10 * t)
b. Determine how many text messages would need to be sent or received to make the cost of the plans equal.
To make the cost of the plans equal, we can set the equation of the first plan equal to the cost of the second plan, which is $40:
$20 + ($0.10 * t) = $40
Now, we subtract $20 from both sides of the equation:
($0.10 * t) = $40 - $20
($0.10 * t) = $20
Lastly, we divide both sides of the equation by $0.10 to solve for t:
t = $20 / $0.10
t = 200
Therefore, 200 text messages would need to be sent or received to make the cost of the plans equal.