Bart’s cell phone package costs $15 a month plus an additional 10 cents per megabyte of data used over his data limit. Ping’s is $10 a month plus 12 cents per megabyte used over her data limit. Determine the data overage when their monthly bills would be the same. Solve with linear system.
To determine the data overage when Bart and Ping's monthly bills would be the same, we can set up a linear system of equations.
Let's represent the data overage in megabytes as x.
For Bart's monthly bill:
Cost = $15 + 0.10x
For Ping's monthly bill:
Cost = $10 + 0.12x
To find when their bills are the same, we set these two expressions equal to each other:
15 + 0.10x = 10 + 0.12x
Simplifying the equation, we get:
0.02x = 5
To solve for x, we divide both sides of the equation by 0.02:
x = 250
Therefore, when Bart and Ping's monthly bills would be the same, the data overage would be 250 megabytes.
To determine the data overage when their monthly bills would be the same, we can set up a linear system of equations using the given information.
Let's assume that x represents the number of megabytes of data used over their respective data limits.
For Bart's monthly bill:
Cost = $15 + $0.10x
For Ping's monthly bill:
Cost = $10 + $0.12x
Since we want to find the point where their bills are the same, we can set up the following equation:
$15 + $0.10x = $10 + $0.12x
Let's subtract $10 and $0.10x from both sides:
$5 = $0.02x
Now, divide both sides by $0.02 to solve for x:
x = $5 / $0.02 = 250 megabytes
Therefore, when Bart and Ping's monthly bills are the same, they have exceeded their respective data limits by 250 megabytes.
15 + 0.10 m = 10 + 0.12 m
0.02 m = 5
m = 5 / 0.02 = 500 / 2 = 250 megabyes