SOLUTION: The sum of a number and it's inverse is 3 29/52 Find the number

Question 1190353: The sum of a number and it's inverse is 3 29/52
Find the number

Answer by greenestamps(13216) (Show Source): You can put this solution on YOUR website!

The sum of a number and its reciprocal is 3 29/52.

Using formal algebra....

let the number be x; then the reciprocal is 1/x

3 29/52 = (156+29)/52 = 185/52

Try factoring that; or use the quadratic formula....

It does in fact factor:

or

ANSWER: The number and its reciprocal are, in either order, 4/13 and 13/4

The answer can be obtained far more easily using logical reasoning, simple trial and error, and easy arithmetic.

(1) Since the sum is a bit more than 3, the larger number must be a bit more than 3.
(2) Since the denominator of the sum is 52, the most likely denominators of the two fractions x and 1/x are 13 and 4.

So try 13/4 and 4/13 for the two numbers and verify that their sum is indeed 3 29/52.

RELATED QUESTIONS
The sum of a number and twice its multiplicative inverse (reciprocal) is 3. Find the... (answered by mananth)

the sum of a number and twice its inverse reciprocal is 3. what is the... (answered by edjones)

The sum of a number and four times its reciprocal is 29/5.Find the number (answered by eggsarecool)

Twice the sum of seven and a number is 52. Find the number. (answered by FrankM)

The sum of a number and 2 times its reciprocal is 3. Find the... (answered by reynard2007)

A two digit number is such that it's value is equal four times the sum of its digits. If... (answered by ikleyn,greenestamps)

The sum of a number and its reciprocal is given below. 29/10. Find the numbers. (answered by sudhanshu_kmr)

the sum of a number and the square of its additive inverse is 72.find the... (answered by solver91311)

In the Dicovering Algebra: An Investigative approach, there is a question that says Find... (answered by jim_thompson5910,stanbon)