Answer:
In 25 minutes, the monthly phone charges of both companies will be the same.
Explanation:
If we allow m to represent the number of minutes, we can create two equations for C, the total cost of phone charges from both companies:
Phoenix equation: C = 0.5m + 30
Nuphone equation: C - 0.10m + 40
Now, we can set the two equations equal to each other. Solving for m will show us how many minutes must Abby use for the total cost at both companies to be the same:
0.5m + 30 = 0.10m + 40
Step 1: Subtract 30 from both sides:
(0.5m + 30 = 0.10m + 40) - 30
0.5m = 0.10m + 10
Step 2: Subtract 0.10m from both sides:
(0.5m = 0.10m + 10) - 0.10m
0.4m = 10
Step 3: Divide both sides by 0.4 to solve for m (the number of minutes it takes for the total cost of both companies to be the same)
(0.4m = 10) / 0.4
m = 25
Thus, Abby would need to use 25 minutes for the total cost at both companies to be the same.
Optional Step 4: Check the validity of the answer by plugging in 25 for m in both equations and seeing if we get the same answer:
Checking m = 25 with Phoenix equation:
C = 0.5(25) + 30
C = 12.5 + 30
C = 42.5
Checking m = 25 with Nuphone equation:
C = 0.10(25) + 40
C = 2.5 + 40
C = 42.5
Thus, m = 25 is the correct answer.