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?
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
The language used for this problem is rather odd. Not at all what I'd expect from a school text.
To find the number of minutes at which these two companies will charge the same, we need to set up an equation and solve for the variable.
Let's denote the number of minutes as "x".
For Company A, the total cost would be the monthly fee plus the cost per minute after 30 minutes:
Total cost for Company A = $25 (monthly fee) + $0.10 (per minute cost) * (x - 30)
For Company B, the total cost would be the monthly fee plus the cost per minute after 30 minutes:
Total cost for Company B = $20 (monthly fee) + $0.12 (per minute cost) * (x - 30)
Now we can set up an equation:
Total cost for Company A = Total cost for Company B
$25 + $0.10 * (x - 30) = $20 + $0.12 * (x - 30)
Let's simplify and solve for x:
$25 + $0.10x - $0.10 * 30 = $20 + $0.12x - $0.12 * 30
$25 + $0.10x - $3 = $20 + $0.12x - $3.60
$0.10x - $0.12x = $20 - $25 + $3.60 + $3
$-0.02x = $1.60
To isolate x, divide both sides by -0.02:
x = $1.60 / $-0.02
x = -80
The answer is x = -80, which means that these two companies will charge the same after 80 minutes of phone calls.
However, it's important to note that negative minutes do not make sense in this context. Therefore, we can conclude that these two companies will never charge the same amount for the given pricing structure.