00:01
In this problem, we have been asked how many solutions there are to the equation x plus y plus z is equal to 20, where each of the integers x, y, and z is at least three.
00:10
So what do we have? we have that x, y, and z, all of them are greater than or equal to three.
00:18
So what we're going to do is assume a to be equal to x minus 3, b to be y minus 3, and c to be z minus 3.
00:31
So in this case, we can see that a, b, and c, they are all going to be greater than or equal to zero.
00:37
This is because x, y, and z are greater than or equal to 3.
00:40
So x minus 3, y minus 3, and z minus 3, they should all be greater than or equal to 0.
00:46
So they're non -negative.
00:47
So now what is our equation? we have x plus y plus z is equal to 20.
00:55
So x is from here, we can see that a is x minus 3.
01:00
So x will be a plus 3.
01:02
So we end up with a plus 3.
01:04
Similarly, y will be b plus 3.
01:07
Z will be c plus 3.
01:08
This is equal to 20.
01:10
So we have a plus b plus c plus 9 is equal to 20...