number of minutes ---- m
solve :
25m = 500 + 15m
solve :
25m = 500 + 15m
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.
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.