A cell phone company offers the
following two plans. Plan A, which is 15 dollars per
month and two dollars for every 300 texts. Plan B, 25 dollars per month and
0.50 dollars for every 100 texts. How many texts would you need to
send per month for plan B to save you money?
Well, the way that we can set up
and solve this problem is to first think, how much does it cost for plan A and plan
B to send 100 texts? Well, if we take a look at plan A,
it costs two-thirds of a dollar per 100 texts. And that’s because of its two
dollars for every 300 texts. Just divide that by three. Then if we look at plan B, we can
see that it’s half a dollar or 50 cents for every 100 texts.
Well, what we can do is we start
set up an inequality. And we could do that because what
we’re gonna have for plan A is 15 plus two-thirds 𝑥, where 𝑥 is the number of
hundreds of texts. Well, we want to see where this is
greater than. And we want to see where it’s
greater than because what we’re trying to do is find out how many texts you’d need
to send per month for plan B to save you money. So we want plan B to be less
than. And then we’ve got for plan B 25
plus a half 𝑥.
So now what we do is we’ve
converted both of our fractions into sixths to make it have a common
denominator. Now we’ve got 15 plus four-sixths
𝑥 is greater than 25 plus three-sixths 𝑥. So now what we’re gonna do is
subtract 15 and subtract three-sixths 𝑥 from both sides of the inequality. And we’re gonna do this because we
want the 𝑥 on one side. And then we want the numeric values
on the other. And when we do that, we’re gonna
get a sixth 𝑥 is greater than 10.
So if we’ve got a sixth 𝑥 is
greater than 10, if we multiply both sides by six, we’re gonna get 𝑥 is greater
than 60. Well, as we said at the beginning,
𝑥 represents the number of hundreds of texts. So therefore, the number of texts
that would need to be sent for plan B to save you money would be greater than 6000
texts. And we get that because we
multiplied 60 by 100, which gives us 6000.