00:01
In this mystery problem, we're once again given three numbers that we don't know, or we're giving relationships with them to try to figure out the values of those numbers.
00:07
So let a equal the first number, let b equal the second, let's equal the third number.
00:13
And then our three given equations are the sum is 105.
00:18
The third number is equal to 10 times the second number, take away 11.
00:23
And the other relationship we're given is that double the first number is equal to three times the second number plus seven.
00:34
And now we can just try to figure out how you use substitution to help solve.
00:39
So with this situation, so it makes sense in this one to try to get everything, i think, in terms of b, because c is already in terms of b, and so we can solve for a pretty easily.
00:50
So if i divide everything by 2, we have a in terms of b as well.
00:54
So i'm just going to say, therefore, divide everything by 2, a must be equal to three halves of b plus seven.
01:05
Seven halves.
01:07
So we know a in terms of b and we know c in terms of b, which means we can write everything in the original sum in terms of b and then solve.
01:18
So let's do that.
01:20
So here we have a, which is three halves, b plus seven halves.
01:30
And then we have b, which is just b.
01:33
And we have c, which is equal to 10b minus 11.
01:38
And all together, so that has to add up to 105.
01:42
So let's just clean that little equation up.
01:45
So that looks right, and then we're good to go.
01:49
All right, so let's get in there and solve this.
01:51
So we can see that we've got like terms combined.
01:54
You've got three halves b, which is one and a half b.
01:58
You've got another 1b here and then 10b.
02:00
So that's 11b plus 1 .5b.
02:03
That's 12 and 1 half b's.
02:05
So you have 12 and 1 half bs.
02:07
The constant we have here is 7 half, which is the same as 3 and 1 half.
02:11
So that's 3 .5.
02:13
And you're taking away 11 from that.
02:15
So you have 3 .5 takeaway 11.
02:19
So that was a little trickier.
02:21
I'll write it out.
02:22
So 11 take away 3 .5.
02:26
And you do that, you're going to get 0 take away is zero, borrow.
02:30
10 take away 5 is 5.
02:32
And then 0 takeaway 3 can't do it.
02:34
Barrow, 10 takeaway 3 is 7.
02:36
So it's 7 .5.
02:37
And you're going to say that that's going to be a negative because the negative wins.
02:41
So it take away 7 .5...