23. There are two telephone companies provide home phone service in New York City. Company A charges $25 monthly fee and $0.10 for one minute after 30 minutes phone call. Company B charges $20 monthly fee and $0.12 for one minute after 30 minutes phone call. By what minutes, these two companies will charge the same?
I have:
A:25.00+0.10(m-30)
B:20.00+0.12(m-30)
For m minutes,
A: 25.00+0.10(m-30)
B: 20.00+0.12(m-30)
So, just solve for m when A=B
Kind of strange wording for a math problem in school. The only way it would make since is if it were 2 part question to the solve for x minutes.
To find the number of minutes at which the two companies will charge the same, we need to set up an equation where the total cost from Company A equals the total cost from Company B.
Let's set up the equation using the given information:
For Company A:
Total Cost from A = $25.00 + $0.10(m - 30)
where m represents the total number of minutes of the phone call.
For Company B:
Total Cost from B = $20.00 + $0.12(m - 30)
To find the number of minutes at which both companies charge the same, we need to solve for m in the equation:
$25.00 + $0.10(m - 30) = $20.00 + $0.12(m - 30)
Now, let's solve this equation step by step:
Step 1: Distribute the coefficients outside the parentheses:
$25.00 + $0.10m - $0.10(30) = $20.00 + $0.12m - $0.12(30)
Step 2: Simplify the equation:
$25.00 + $0.10m - $3.00 = $20.00 + $0.12m - $3.60
Step 3: Combine like terms:
$22.00 + $0.10m = $16.40 + $0.12m
Step 4: Subtract $0.10m and $16.40 from both sides of the equation:
$22.00 - $16.40 = $0.12m - $0.10m
Step 5: Simplify and solve for m:
$5.60 = $0.02m
Step 6: Divide both sides of the equation by $0.02 to isolate m:
m = $5.60 / $0.02
Step 7: Simplify to find the number of minutes at which both companies charge the same:
m = 280
Therefore, the two companies will charge the same after 280 minutes of phone call.