00:01
In this question, we are told that the sum of three numbers is 123.
00:06
We are also told that the second number is 9 less than 2 times the first number.
00:14
The third number is 6 more than 3 times the first number.
00:19
And we are asked to find the numbers x, y and z.
00:22
So, y is 9 less than 2 times x? basically means that if we multiply x by 2, then y is going to be 9 less than that number.
00:34
So if we subtract 9 from 2x, we are going to get y.
00:45
So because y is 9 less than 2 times x, right? so we multiplied x by 2, subtracted 9, and we've gotten y.
00:56
Z is 6 more than 3 times x.
01:01
So if we multiply x by 3, then we still have to add 6 more to get z.
01:12
And the last equation is the first equation.
01:16
X plus y plus z, the sum of the three numbers equals to 123.
01:20
This gives us a system of equations for finding x, y and z.
01:25
And what we are going to do next, we will plug in y and z from the first two equations into the last equation.
01:36
So we will just rewrite the first two equations.
01:48
And in the last equation, we are going to get x plus 2 x.
01:53
X minus 9 plus 3x plus 6 equals to 123.
02:04
Now the last equation contains only x, which would simplify to 6x minus 3 equals to 123...