00:01
In this problem, we will work with the concept of systems of linear equations.
00:08
This problem is going to ask us to write or require that we write a system of three linear equations in three variables.
00:18
And we will use the elimination method to solve this system.
00:24
As with any application problem, you should always start by representing your unknowns with variables.
00:32
Telling what each variable does stand for.
00:35
So i'm going to start off with this problem and do that.
00:38
Okay, now over here i have a summary of the information in the problem.
00:44
It involves shipping charges of $4, shipping charges of $8, and shipping charges of $10 depending on this amount of money spent on the various orders or the cost of the various orders.
00:59
So what i'm going to do on this problem, i'm going to let x represent the number of orders shipped at $4.
01:11
So let's say orders shipped at $4.
01:27
I'm going to let y represent the orders shipped at $8.
01:37
The number of orders that the shipping charges was $8.
01:48
And then z will be the number of orders shipped at $10.
02:06
Once you have expressed your variables and what each one represents, then you will use the information in the problem to set up your equations.
02:16
And as i said earlier, this is a system that will use three linear equations and three variables.
02:23
So i should be able to use the information and set up three equations.
02:29
So as i look at this summary, i see that there was a total of 600 orders.
02:36
Well, that's information that allowed me to write the first equation.
02:40
If x, y, and z each stand for the number of orders at the various rates, then i should be able to write the equation x plus y plus z is equal to 600.
02:57
Okay, then i also know the total shipping charge.
03:00
Of these 600 orders was $4 ,280.
03:07
So with that, what i will do is take the number of orders at each rate and multiply times the charge for that.
03:18
So i start off with 4 times x, so that's how much money or the shipping charges for x orders at $4 an order.
03:30
In a similar way i'll have an 8y and then i'll have a 10c that i'll add together and set it equal to the total shipping charges of $4 ,280.
03:46
Then for the third equation i will take this information that says there are 80 more orders for $25 or more or less, i'm sorry, than for those they're over $75.
04:02
Dollars so for this equation i will let x since that's going to be the four dollar orders that's when the order was $25 or less so i'll let x equal 80 more orders than those that was over $75 so those over $75 were the $10 orders and the $10 orders is represented by z so i've got 80 plus z now when you're solving a system of linear equations and you're going to use elimination, it's often helpful to have the equations in more of a standard form.
04:46
So i'm going to take my third equation and i'm going to subtract z from each side and i will get x minus c equals 80, which is an equation that's equivalent to x equals 80 plus z...