1) Take any number
2) Multiply your number by 6
3) Add_________
4) Divide by __________
5) Subtract the number you started with
A) Complete 3 & 4 so that the expected outcome will always be 7.
B) Use Algebra to explain how your trick works.
Solution to the Problem:
(A) Add 42 and Divide by 6 so that you will always get 7.(B) Here is the algebra:
1) Let x = number
2) Multiply your number by 6, then you get 6x
3) Add 42, so you would get 6x + 42
4) Divide by 6, so you would get (6x + 42) / 6 which simplifies to x + 7
5) Subtract the number you started with, so you get (x + 7) - x = 7
I used algebra to figure out the values of A and B to make this work:
1) Let x = number
2) Then you get 6x
3) Add A, so you would get 6x + A
4) Divide by B, so you would get (6x + A) / B
5) Then you get ((6x + A) / B) - x
Now set this expression equal to 7:
((6x + A) / B) - x = 7
Multiply by B: (6x + A) - Bx = 7B
you want this to work for any values of x, so I would make B = 6 to get rid of the x's.
Then you get 6x + A - 6x = 7(6)
This yields A = 42.
It works for any values of x.
1) For example, x = 8
2) Then multiplying by 6, you get 48,
3) Add 42 to get 90
4) Divide by 6 to get 15
5) Subtract the original number 8 to get 7.
Correctly solved by:
| 1. 유순호 (Soonho You) | JeonJu, South Korea |
| 2. Ivy Joseph | Pune, Maharashtra, India |
| 3. James Alarie | Flint, Michigan |
| 4. Bernice Rosales |
Delta High School, Delta, Colorado |
| 5. Brijesh Dave | Mumbai City, Maharashtra, India |
| 6. Angelica Mosher |
Mountain View High School, Mountain View, Wyoming |
| 7. Adam Bates |
Mountain View High School, Mountain View, Wyoming |
| 8. Anonymous | New York, New York |
| 9. Kelly Stubblefield | Mobile, Alabama |