The recipocal of 4 less than a number is three times the reciprocal of the same number.What is the number?

let the number be x

1/(x-4) = 2(1/x)

solve for x

x=8

Well, let's break it down:

The reciprocal of a number is just 1 divided by that number. So, if we let the number be "x", the reciprocal of "x" would be 1/x.

According to the problem, the reciprocal of 4 less than the number is three times the reciprocal of the same number. So, mathematically, we can write it as:

1/(x - 4) = 3 * (1/x)

Now, let's solve this equation...or maybe we could call a math magician to solve it. Do you happen to know any?

But seriously, let's continue:

Multiplying both sides of the equation by x * (x - 4) to get rid of the denominators, we get:

x = 3 * (x - 4)

Now let's distribute:

x = 3x - 12

Subtracting x from both sides:

0 = 2x - 12

Adding 12 to both sides:

12 = 2x

Dividing both sides by 2:

x = 6

So, the number is 6.

To find the number in this problem, we need to set up an algebraic equation based on the given information.

Let's assume the number is x.

According to the problem, the reciprocal of 4 less than the number is three times the reciprocal of the same number.

The reciprocal of a number x is 1/x. So, the reciprocal of 4 less than the number is 1/(x - 4).

According to the problem, this reciprocal is three times the reciprocal of the same number. Therefore, we can write the equation as:

1/(x - 4) = 3 * (1/x)

Now, we can solve this equation to find the value of x.

Multiplying both sides of the equation by (x - 4) * x to eliminate the denominators:

(x - 4) * x * [1/(x - 4)] = (x - 4) * x * [3 * (1/x)]

Cancelling out the common factors:

x = 3 * (x - 4)

Expanding the right side of the equation:

x = 3x - 12

Bringing all the terms with x to one side of the equation:

x - 3x = -12

Simplifying:

-2x = -12

Dividing both sides of the equation by -2:

x = -12 / -2

Simplifying further:

x = 6

Therefore, the number is 6.