I am a number. If you add me to 952 and then subtract 167, I become 822. What number am I?
We might call this sort of problem a mystery number problem because we’re starting with a number that we don’t know. In fact, we need to find out what this starting number is. That’s what the question is asking us to do.
We can think of problems like this as being a little bit like number machines. In goes our mystery number. First, we’re told to add it to 952 then to subtract 167. And then the number that comes out the other end is 822. If we wrote a number sentence, it would look like this. Something plus 952 take away 167 equals 822.
So to find our missing number, we need to start with 822 and work our way backwards. To work our way backwards, we need to complete the inverse operation or the opposite operation to each step. So if we’re working backwards through our number machine, instead of taking away 167, we need to add 167. And then instead of adding 952, we need to take 952 away. By using the inverse operations and working backwards like this, we can find the starting number.
So if we write this calculation as a number sentence, it will read 822 plus 167 take away 952 equals the number that we’re looking for. So let’s complete our two steps. First of all, we’re going to add 822 and 167. Two plus seven equals nine, 20 plus 60 equals 80, and 800 plus 100 equals 900. So at this point in our number machine, the number is 989.
Now let’s complete the second step. We need to take away 952 from our number, 989 take away 952. Nine take away two is seven, and eight take away five is three. So we know 80 take away 50 is 30. And there’s nothing left in the hundreds column. 900 take away 900 equals zero.
So our number at the start of our number machine is 37. This is the number that our problem talks about. Let’s read through our problem again, this time the way it’s supposed to be read and this time using the number that we know we start with, which is 37. And instead of adding 167, we need to subtract 167.
I am a number. We know it’s the number 37. If you add me to 952 — we know we get the answer 989 — and then subtract 167, I become 822. It might be a good idea to pause the video and to check that that works. Does 37 add 952 take away 167 equal 822? It should do. We worked backwards and used inverse operations to find the missing starting number. And that number is 37.