when is .15t + 26.50 = .25t + 14.50
multiply by 100 to clean up the numbers
15t + 2650 = 25t + 1450
-10t = -1200
t = 120 minutes
at 120 minutes the charge would be the same
One cellular phone carrier charges $26.50 a month and $0.15 a minute for local calls. Another carrier charges $14.50 a month and $0.25 per minute for local calls. For how many minutes is the cost of the plans the same?
2 answers
The answer given “120 minutes” is incorrect.
This question is determined not only by math but also by grammar. The question was not “at how many minutes…” or “at what time…”. The question was “for how many minutes…”
“For” indicates duration. In order to ask the moment at which the charges would equalize, the question would need to be worded using “at,” indicating a specific time when this was to occur. Since the author instead used the word “for,” the meaning instead is about duration.
For example: at what time…? At how many miles…? At what distance…?
As opposed to: for how much time…? For how many miles…? For what distance…?
So, rather than “120 minutes,” which is the moment at which the two phone companies are charging the same rate, the correct answer is “1 minute,” which is the length of time at which the two phone companies are charging the same rate. For the first 119 they charged differently, and from 121 on they will again be charging differently.
This question is determined not only by math but also by grammar. The question was not “at how many minutes…” or “at what time…”. The question was “for how many minutes…”
“For” indicates duration. In order to ask the moment at which the charges would equalize, the question would need to be worded using “at,” indicating a specific time when this was to occur. Since the author instead used the word “for,” the meaning instead is about duration.
For example: at what time…? At how many miles…? At what distance…?
As opposed to: for how much time…? For how many miles…? For what distance…?
So, rather than “120 minutes,” which is the moment at which the two phone companies are charging the same rate, the correct answer is “1 minute,” which is the length of time at which the two phone companies are charging the same rate. For the first 119 they charged differently, and from 121 on they will again be charging differently.
1 answer