Posted by **Angie** on Monday, September 22, 2008 at 7:54pm.

1. A very magical teacher had a student select a two-digit number between 50 and 100 and write it on the board out of view of the instructor. Next, the student was asked to add 76 to the number, producing a three-digit sum. If the digit in the hundred’s place is added to the remaining two-digit number and this result is subtracted from the original number, the answer is 23, which was predicted by the instructor. How did the instructor know that the answer would be 23?

- Math -
**Angela**, Monday, September 22, 2008 at 7:58pm
i don't get it

- Math -
**Raymond**, Sunday, June 12, 2011 at 10:46pm
Just convert the word problem to a number problem.

Let x = the number that you choose between 50 and 100.You add 76 to x or x+76 then you take the hundreds place digit away from its place in the sum of the 2 numbers and add it to the x+76. This is the same as subtracting 99 from the x+76 Why? Because you moved the hundreds place number out of its place. Its no longer there and you add it as a 1 to x+76. That is the same as adding (-100+1) or -99 to the x+76 so, knowing this, lets see how it would look in purely numeric form. Choose a number x between 50 and a hundred. Add 76 to it x+76 then x+76-99 =x-23. Subtract this number from your original number x or x-(x-23) or x-x+23 then the x's cancel each other out and the only thing remaining is 23. The key factor is how much you add to your original number. if instead of adding 76 I added 89 then the result would always be 10 assuming you followed the rest of the guidelines.

- Math -
**JACOB**, Wednesday, August 26, 2015 at 3:53pm
ITS 88

## Answer This Question

## Related Questions

- physics - A 750-N physics student carries a 4.0 meter board, uniform in shape, ...
- english - "Once hired, the teacher will sign a contract with the board of ...
- Statistics - A group of freshmen and sophomore students was selected and each ...
- Algebra HELP! - A teacher instructed her class to take any number and perform a ...
- math - In a class of 60 student,the number of student who passed biology is 6 ...
- math - An instructor counts homework as 1/3 of the student's grade and the ...
- algebra - : a student scored 73 out of 100 on a test. If the maximum score on ...
- mat/116 - a student scores 74 out of 100 on a test. if the maximum on the next ...
- math - Mr. digit wanted to assign a number to each student in his class. He ...
- Math - Mr. Digit wanted to assign a number to each student in his class. He ...

More Related Questions