If four times the reciprocal of a number is added to one-fifth of its reciprocal,the result equals 3. What is the number

Answer 1

You can solve this question with the following equation:

4(1/x) + (1/5)(1/x) = 3

4/x + 1/(5x) = 3 (multiply by the LCD (5x) to eliminate the fractions)

20 + 1 = 15x

21 = 15x

15x = 21

x = 21/15 (simplify dividing by 3)

x = 7/5

Answer 2

Let r = the reciprocal of the number. Then

4r + r/5 = 3

20r + r = 15

21r = 15

r = 15/21 = 5/7

Therefore, the number is 1/r = 7/5.

You could also let the number be n, for example, and write 4(1/n) + (1/n)/5 = 3 and get the result directly for n, but may be trickier with more fractions.