Question

repeat the following procedure for the four given numbers. multiply the number by 2. add 10 to the product. divide the sum by 2. subtract 5 from the quotient. the first number is 2, the 2nd number is 4, the 3rd number is 8,the 4th number is 10

Answer 1

Lets start with the first case (the number is 2). Then, we get

Now, for the second case (the number is 4), the result is

Now, for 3rd case ( the number is 8), we have

And for 4th case (the number is 10) we get

a) As we can note, the result is always the same number we started with.

Then, if we represent the first number by n, the result is n.

b) Let n be the given number, then, we can write:

-Multiply the number by 2:

`2n`

-Add 10 to the product:

`2n+10`

- Divide the sum by 2:

`(2n+10)/(2)`

but this is equal to

`(2n+10)/(2)=(2n)/(2)+(10)/(2)=n+5`

- Substract 5 from the quotient:

`(2n+10)/(2)-5`

but (from our last result) this is equal to

`n+5-5=n`

which is our first number n. Thats why the answer in all cases is the same number we started with.