suppose that the Aztec cell phone company charges $50 per month plus 15 cents per minute while the southern cell phone company charges no monthly fee but 25 cents per minute after how many minutes of phone usage would a monthly phone bill be the same from both companies
number of minutes ---- m
solve :
25m = 500 + 15m
suppose that the Aztec cell phone company charges $50 per month plus 15 cents per minute while the southern cell phone company charges no monthly fee but 25 cents per minute after how many minutes of phone usage would a monthly phone bill be the same from both companies
To find the number of minutes of phone usage where the monthly bill is the same from both companies, we can set up an equation.
Let's denote the number of minutes of phone usage as "x".
For Aztec Cell Phone Company, the monthly bill is given by:
Bill_Aztec = $50 (fixed monthly fee) + $0.15 (per minute charge) * x
For Southern Cell Phone Company, the monthly bill is given by:
Bill_Southern = $0 (no monthly fee) + $0.25 (per minute charge) * x
To find when the monthly bills are the same, we set the two equations equal to each other and solve for x:
$50 + $0.15x = $0 + $0.25x
Simplifying the equation:
$0.15x - $0.25x = -$50
-$0.10x = -$50
Dividing both sides by -$0.10:
x = -$50 / -$0.10
x = 500
Therefore, after 500 minutes of phone usage, the monthly phone bill would be the same for both companies.
To find the number of minutes at which the monthly phone bill becomes the same for both companies, we need to set up an equation and solve for the unknown variable, which in this case is the number of minutes.
Let's start by understanding the cost equation for each company:
1. Aztec Cell Phone Company:
The monthly cost is a fixed fee of $50 plus an additional cost of 15 cents per minute. Thus, the cost equation for Aztec can be written as:
Cost_Aztec = 0.15 * minutes + 50
2. Southern Cell Phone Company:
There is no monthly fee; the cost is solely based on the number of minutes used, charged at a rate of 25 cents per minute. The cost equation for Southern can be written as:
Cost_Southern = 0.25 * minutes
Now, let's set up the equation and solve for the minutes of phone usage where the monthly phone bill becomes the same:
0.15 * minutes + 50 = 0.25 * minutes
To solve this equation, we can rearrange it as follows:
0.15 * minutes - 0.25 * minutes = -50
-0.10 * minutes = -50
Divide both sides of the equation by -0.10 to isolate 'minutes':
minutes = -50 / -0.10
Simplifying further:
minutes = 500
So, after 500 minutes of phone usage, the monthly phone bills from both the Aztec and Southern cell phone companies would be the same.