Waneek picks a two-digit number, subtracts the tens digit and then subtracts the ones digit to get a new number.
For example if she had picked 37, she would get
37 - 3 - 7 = 27
so her new number would be 27.
How many different numbers can be formed using Waneek's process?
its 5
Let x be the 10s digit.
Let y be the 1s digit.
So any two digit number is represented by 10x + y.
Subtracting the 10s digit and then the 1s digit gives 10x + y - x - y = 9x
So resulting numbers are all multiples of 9, regardless of which 2 digit number we start with.
The lowest value x can be is 1, giving a result of 9.
The highest value x can be is 9, giving a result of 81.
Filling in the remaining multiples of 9, we have 9 numbers that can be formed from Waneek's process:
9,18, 27, 36, 45, 54, 63, 72, and 81.
To understand how many different numbers can be formed using Waneek's process, we need to break down the problem step by step.
Waneek picks a two-digit number. Since a two-digit number can have any digit from 0 to 9 in both the tens and ones place, there are 10 options for each digit.
After picking the two-digit number, Waneek subtracts the tens digit and then subtracts the ones digit to get a new number.
Let's consider an example to illustrate the process further. Suppose Waneek picked the number 59.
- She subtracts the tens digit, which is 5, from 59: 59 - 5 = 54.
- Then, she subtracts the ones digit, which is 9, from 54: 54 - 9 = 45.
So, starting with the number 59, Waneek obtains the new number 45.
Now, let's analyze the possibilities for different numbers using this process systematically:
For the tens digit:
- If Waneek chooses 0 as the tens digit, there are 10 options for the ones digit (0 to 9).
- If she chooses 1 as the tens digit, there are also 10 options for the ones digit (0 to 9).
- If she chooses 2, 3, 4, 5, 6, 7, 8, or 9 as the tens digit, there will still be 10 options for the ones digit.
Since there are 10 options for the tens digit in all cases, and for each of those options, there are 10 options for the ones digit, the total number of different numbers that can be formed using Waneek's process is 10 * 10 = 100.
Therefore, Waneek can form 100 different numbers using her process.