00:01
All right.
00:01
So in this problem, someone buys some radios for $1 ,200.
00:05
We don't know how many there are.
00:07
Then this dealer sells half of them and gives half of them away.
00:14
When she sells the half that she does end up selling, she charges $10 more per radio.
00:20
And the result is a net balance or breaking even.
00:26
So i've set up the same type of model that we've been using all throughout.
00:31
This particular section.
00:33
The rate at which she bought them, we don't know, but the rate at which she sold them was $10 more per radio.
00:44
The number of radios that she bought, we don't know.
00:53
The number of radios that she sold was half of the number that she bought.
00:59
And the total for each is $1 ,200.
01:03
Now, there might be a better way to go.
01:05
About this, but this is the way that it made sense to me based off of the setup.
01:11
So now i'm going to write these two equations.
01:13
R multiplied by n is equal to 1 ,200, and r plus 10 multiplied by half of n is equal to 1 ,200.
01:31
Next, i'm going to solve for one of the variables in this first equation, which is by far the least complicated of the two.
01:39
And i'm going to show what happens in either of the situation.
01:46
So the first is that we want to solve for n.
01:48
If i want to solve for n, then i'm going to get n by itself by dividing by r.
01:53
And so n is equal to 1 ,200 divided by r.
02:02
A different way that i could approach this is instead solving this equation for r.
02:09
So r is equal to 1 ,200 divided by n.
02:15
Then i'm going to substitute whichever situation into the other equation, the one for selling.
02:24
So in this case, if n is 1 ,200 over r, then that's what goes in the place of n here.
02:32
So this is r plus 10 times the quantity 1 ,200 over r half, which is equal to 1 ,200.
02:54
All right? that is incredibly complicated looking.
02:58
So i'm going to start by multiplying both sides by 2.
03:04
So if i multiply this side by 2, the 2s will cancel out...