00:01
So in this problem, we're told that the wife went to the store and bought three packets of bacon and four cartons of eggs and it cost her $14 .13.
00:08
And then the husband, who didn't know she went to the store, he bought four packages of bacon and three cartons of eggs and it cost him $15 .83.
00:17
So now they want to return some of this.
00:19
They're going to return three packages of bacon and three cartons of eggs.
00:23
We want to figure out what their refund was going to be.
00:26
Well, first, we have to find the cost for both.
00:28
So what we're going to do is set up a system of equations.
00:33
So i'm going to let b represent bacon and e represent eggs.
00:37
Well, we know that three packages of bacon, so three times b, plus four cartons of egg, so four times e, would equal to $14 and $13.
00:46
Now we'll come up an equation for the husband.
00:49
Well, he got four packages of bacon plus three cartons of eggs and that equal to $15 .83.
00:55
So now we just need to solve the system of equations.
00:58
Well, i'm going to do this by elimination.
01:01
So to eliminate the bs, i'm going to make one of them 12 and one negative 12.
01:05
So to do this, i'm going to multiply the first equation by 4 and the second equation by negative 3.
01:10
So for the first equation, when we distribute the 4, 4 times 3b, that's 12b.
01:16
4 times 4e is 16e.
01:18
And then we have 4 times $14 and 13, which is equal to $56 and 52.
01:26
Now we'll distribute to negative 3.
01:28
Negative 3 times 4b is negative 12b.
01:31
Negative 3 times 3e is negative 9e.
01:35
And then we're going to have negative 3 times $15 .83, which is equal to negative $47 and 49 cents.
01:43
So now we can go ahead and add the two equations because 12b minus 12b is equal to 0.
01:49
So these terms will cancel...