On Chatty Cathy’s cell phone plan she pays for minutes used plus a fixed monthly charge. For 500 minutes she pays $35 total, and for 1500 minutes used she pays $55 total.
What is her monthly fixed charge?
A) $15
B) $20
C) $25
D) $30
y = mx+b, so
500m+b = 35
1500m+b = 55
so,
1500m+3b = 105
1500m+b = 55
2b = 50
b = 25
To find Chatty Cathy's monthly fixed charge, we need to determine the difference in cost between the two scenarios.
Let's calculate the cost per minute for each scenario:
For 500 minutes at $35 total:
Cost per minute = $35 / 500 minutes
Cost per minute = $0.07
For 1500 minutes at $55 total:
Cost per minute = $55 / 1500 minutes
Cost per minute = $0.0367
Now, let's subtract the cost per minute for the 1500-minute scenario from the cost per minute for the 500-minute scenario to find the monthly fixed charge:
Monthly fixed charge = Cost per minute for 500-minute scenario - Cost per minute for 1500-minute scenario
Monthly fixed charge = $0.07 - $0.0367
Monthly fixed charge = $0.0333
To convert this to dollars, we will multiply by 100:
Monthly fixed charge = $0.0333 * 100
Monthly fixed charge = $3.33
Therefore, her monthly fixed charge is $3.33, which rounded to the nearest dollar, is $3. The answer is not provided in the options, so none of the given options are correct.
To find the monthly fixed charge on Chatty Cathy's cell phone plan, we can set up a system of equations using the given information.
Let's call the fixed monthly charge "x" and the charge per minute "y".
According to the first scenario, for 500 minutes, Chatty Cathy pays a total of $35. Therefore, we can write the equation as:
500y + x = 35
According to the second scenario, for 1500 minutes, Chatty Cathy pays a total of $55. We can write the equation as:
1500y + x = 55
Now, we have a system of two equations:
500y + x = 35 ----(1)
1500y + x = 55 ----(2)
To find the monthly fixed charge, we can solve this system of equations. Let's use the method of substitution.
First, let's solve equation (1) for x:
x = 35 - 500y
Now, substitute this value of x into equation (2):
1500y + (35 - 500y) = 55
1500y + 35 - 500y = 55
1000y + 35 = 55
1000y = 20
y = 20/1000
y = 0.02
Now, substitute the value of y back into equation (1) to find x:
500(0.02) + x = 35
10 + x = 35
x = 35 - 10
x = 25
Therefore, Chatty Cathy's monthly fixed charge is $25.
So the answer is C) $25.