Question

Think of a number, subtract 7, multiply 3, add 30, divide by 3. Then subtract the original number. The result will always be 3. Use polynomials to illustrate this trick.

Answer 1

Soution:

Let the number be x.

According to the question, first step is to subtract 7 from original number.

∴ x-7

Then, multiply the result with three.

∴ (x-7)*3 = 3x-21

Then, add 30 to it.

∴ 3x-21+30 = 3x+9 = 3(x+3)

Then, divide it by 3.

∴ 3(x+3)/3 = x+3

Finally, subtract the original number.

∴ x+3-x = 3

⇒The result will always be 3.

Hence Proved

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Answer 2

Given: A number of mathematical operations on any assumed number

To find: To prove the result will always be 3

Solution: Let this number be x.

Subtracting 7 from it ⇒ (x - 7).

Multiplying the above expression with 3 ⇒ 3(x - 7)

Adding 30 to the above expression ⇒ 3(x - 7) +30

Dividing the above expression by 3 ⇒ {3(x - 7) + 30}/3

Subtracting the original number from the above expression⇒{3(x-7) + 30}/3 - x

Solving the above expression ⇒

{3(x - 7) + 30}/3 - x

= (x - 7) + 10 - x

= 3

Hence proved, the result will always be 3.