00:01
For this problem, we have that a gym membership with two personal training sessions costs $125, while the same gym membership with five personal training sessions costs $260.
00:15
So the question is, what is the cost per training session? well, we have right here is a system of linear equations.
00:25
So first i'm going to pick two variables, one for the cost of the membership, and then one for the cost of each training session.
00:34
Then we'll create our two equations with two unknowns, and then we'll solve that system.
00:40
Okay, so let's get started.
00:43
I'm going to let m be the cost of the membership, and i'm going to let t be the cost per training session.
00:51
So now that we have our variables, we can go ahead and create our equations.
00:55
The first half of the first sentence gives us one equation.
00:59
We have that the gym membership, so m, plus two training sessions, so plus two t, is going to equal or cost us $125.
01:12
So here is our first equation.
01:14
M plus 2t is equal to 125.
01:18
Now the second half of that sentence will give us information for our second equation.
01:23
We have that the same membership, so m plus five training sessions, so 5 t, so 5 t, is now going to equal $260.
01:35
So we have m plus 5t is equal to 260.
01:40
And this is the system that we're going to try to solve.
01:44
Now there's a number of different things that we could do, or a number of different methods to try to solve a system of equations.
01:52
The way that i did it, it was the one that popped out at me at the most.
01:57
I notice that we have an m and an m here.
02:00
They're both just m's.
02:01
So what i'm actually going to do is i'm going to multiply the top equation by negative 1 on both sides of the equation.
02:11
And you'll see in a moment why i'm going to do so.
02:13
So i'm going to multiply everything by negative 1 here...