00:01
For this question, we're given that a three -digit number x is equal to 11 times the two -digit number formed by using a hundred's digit and the units digit of x in the tens place and the units place respectively.
00:15
If the hundred's digit and the tens digit of x differ by one, what is the unit's digit? so in order to answer this question, we need to start by defining our variables.
00:26
First, we're given in the problem that the three -digit number is x.
00:32
So we can define the variable x to be the three -digit number.
00:41
Now, within this three -digit number, i'm going to let a be the digit in the hundreds place.
00:48
B will be the digit in the tens place.
00:54
And c will be the digit in the one's place.
01:00
So now that we've defined the variables, let's look back at the problem.
01:04
And use the information provided to write equations.
01:08
First of all, we're given that the three -digit number x is equal to 11 times the two -digit number formed by using the hundreds digit and the units digit of x in the 10's place and units ' place, respectively.
01:23
So we can write the equation that x is equal to 11 times 10a plus c.
01:32
Since we know that a is the digit in the hundreds place, and c is the digit in the one's place.
01:40
Now, since the digit a is in the 10's place, we need to multiply it by 10, and the unit digit does not need to be multiplied by anything.
01:50
Now, we're also given that the hundreds digit and the 10's digit differ by 1.
01:55
This allows us to write the equation b minus a equals 1, since we know that b is the 10's digit and a is the 100s digit, and the difference is 1...