Frank's cell phone package costs $20 per month and an additional $0.05 per text. Josie pays $15 per month and $0.10 per minute. Determine the linear system that could be used to find out when their monthly bills would be the same.
Let's define the variables:
Let x be the number of text messages Frank sends in a month.
Let y be the number of minutes Josie uses in a month.
The cost of Frank's cell phone package is given by:
C(Frank) = $20 + $0.05x
The cost of Josie's cell phone package is given by:
C(Josie) = $15 + $0.10y
To find out when their monthly bills would be the same, we need to set their costs equal to each other:
C(Frank) = C(Josie)
$20 + $0.05x = $15 + $0.10y
This gives us the linear system:
0.05x - 0.10y = $15 - $20
0.05x - 0.10y = -$5
So, the linear system that could be used to find out when their monthly bills would be the same is:
0.05x - 0.10y = -$5
To determine the linear system that could be used to find out when Frank's and Josie's monthly bills would be the same, let's first define the variables:
Let x represent the number of texts Frank sends in a month.
Let y represent the number of minutes Josie talks in a month.
Frank's monthly bill can be determined by the equation:
Frank's Bill = $20 (base cost) + $0.05 (cost per text) * x
Josie's monthly bill can be determined by the equation:
Josie's Bill = $15 (base cost) + $0.10 (cost per minute) * y
Now, since we want to find out when their monthly bills would be the same, we can set up the following linear system:
Frank's Bill = Josie's Bill
$20 + $0.05x = $15 + $0.10y
Simplifying the equation:
$0.05x - $0.10y = $15 - $20
$0.05x - $0.10y = -$5
So, the linear system that could be used to find out when their monthly bills would be the same is:
0.05x - 0.10y = -5