Question

The sum of a positive number and 31 is 140 times the reciprocal of the number. Find the number. (Hint: The reciprocal of x is 1/x )

Answer 1

To find the positive number, we set up an equation and solve for x. The number is 4.

Step-by-step explanation:

To solve this problem, we need to set up an equation based on the information given.

Let's call the positive number x. The sum of the positive number and 31 is 140 times the reciprocal of the number.

So, the equation is:

x + 31 = 140 * (1/x).

To solve this equation, we can start by multiplying both sides by x to eliminate the fraction:

x^2 + 31x = 140.

Rearranging the equation, we get

x^2 + 31x - 140 = 0.

Now we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.

The factored form of the equation is

(x + 35)(x - 4) = 0,

which gives us two possible solutions:

x = -35 or x = 4.

However, since the problem specifies that the number must be positive, we can discard the negative solution. Therefore, the number is 4.