Question

if 3 is subtracted from a whole number the result is 18 times the reciprocal of the number. find the number​

Answer 1

Let's assume the whole number is represented by
`\displaystyle x`.

According to the problem statement, if we subtract 3 from the whole number, the result is equal to 18 times the reciprocal of the number. Mathematically, this can be expressed as:

`\displaystyle x-3=18\cdot (1)/(x)`

To find the value of
`\displaystyle x`, we can solve this equation.

Multiplying both sides of the equation by
`\displaystyle x` to eliminate the fraction, we get:

`\displaystyle x^(2) -3x=18`

Rearranging the equation to standard quadratic form:

`\displaystyle x^(2) -3x-18=0`

Now, we can factor the quadratic equation:

`\displaystyle ( x-6)( x+3)=0`

Setting each factor to zero and solving for
`\displaystyle x`, we have two possible solutions:

`\displaystyle x-6=0\quad \Rightarrow \quad x=6`

`\displaystyle x+3=0\quad \Rightarrow \quad x=-3`

Since the problem states that the number is a whole number, we discard the negative value
`\displaystyle x=-3`. Therefore, the number is
`\displaystyle x=6`.

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