A positive number when decreased by 4 is equal to 21 times the reciprocal of the number. Find the number?

Let's denote the number as x.

The problem can be translated into the following equation:

x - 4 = 21 * (1/x)

To solve this equation, we can first multiply each side by x to get rid of the fraction:

x^2 - 4x = 21

Then, we can rearrange the equation to set it equal to zero:

x^2 - 4x - 21 = 0

This is a quadratic equation in the form of ax^2 + bx + c = 0. We can solve it by factoring:

(x - 7)(x + 3) = 0

Setting each factor equal to zero gives the solutions x = 7 and x = -3.

However, the problem specifies that the number is positive, so the number we are looking for is x = 7.

Sure, let's solve this step by step.

Step 1: Let's denote the number we are looking for as x.

Step 2: According to the problem, the number decreased by 4 is equal to 21 times the reciprocal of the number. We can write this as an equation: x - 4 = 21*(1/x).

Step 3: To solve for x, we first need to get rid of the fraction. We can do this by multiplying every term by x, which gives us: x^2 - 4x = 21.

Step 4: This is a quadratic equation, and we can solve it by first moving all terms to one side of the equation: x^2 - 4x - 21 = 0.

Step 5: Now we can factor the quadratic equation: (x - 7)(x + 3) = 0.

Step 6: Setting each factor equal to zero gives the solutions x = 7 and x = -3.

Step 7: However, the problem specifies that the number is positive, so the only solution is x = 7.