November 2019
Problem of the Month

Number Trick

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

Send any comments or questions to: David Pleacher