Calculating for unknown number using partial information |
 This shows that give the number 2345, you will be able to decompose it into 5 ones, 4 tens, 3 hundreds and 2 thousands. Now we will take a look at how you can use this knowledge to find a mystery number if you only given partial information. To be able to take full advantage of this lesson you should familiarize yourself with basic linear equations and simultaneous equations. Example 1: Info: I have a 2 digit number. Their sum is 8. I have 6 tens. What is the mystery number? To get to the number, we must first look at what is known about this number that we will express as xy (because it is a two digit number. Here is what we know:  Using what is known, we can solve for this number as follows:  From this we can prove that 6 + 2 = 8 and thus the mystery number is 62 I have a 2 digit number. Their difference is 2. My ten digits are greater than my one digits. I have 3 ones. What is my mystery number? Again here is what is known about this number:  Note here that we know the value of y to be 3, thus we can solve for x as follows:  Thus, from this we can conclude that our mystery number is 53 Example 3: info: I have a 2 digit number. The sum of the digits is 9. Their difference is 3. I have more tens than ones. What is known about this number?  and x > y Using what we learned from solving simultaneous equations, we can solve for x as follows:  Now that we know the value of x, we cam solve for y by substituting 6 for x in one of the known facts: 6 + y = 9, thus y = 9 - 6 and y = 3. To prove it:  Thus, our mystery number is 63 |
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