00:01
The topic of this question is systems of linear equations.
00:06
Here we have a situation about a restaurant that needs 200 new sets of dishes.
00:14
They want to buy the restaurant manager wants to buy two different designs of dishes with the $7 ,400 available.
00:34
So given these 200 sets that need to be bought, how many of each design should be bought? so to figure out the number of design one sets and the number of design two sets, let's give these numbers names, that is, variables.
01:00
Call them x and y.
01:03
So let x be the number of design one sets of dishes, and the n .y be the number of sets of design two.
01:13
Now we have to form two equations to solve for these two unknowns.
01:20
Remember that we want 200 sets in total and so the number of a design two sets plus the number of design one sets should be 200 and we also have a total of 7 ,400 to spend so the total amount spent on design one sets of dishes plus the total amount of money spent on design two sets of dishes should equal 7 ,000 $400.
02:09
So let's figure out what these amounts should be.
02:14
If we need x, design 1 sets, and each costs $25, then the total amount spent on design 1 sets is 25x.
02:33
X sets for $25 a set is $25x dollars altogether.
02:42
Similarly, since we want y design two sets, at $45 per set, we're going to need to spend $45 y on these sets altogether...