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Question

One seventh of a number added to one third of the same number is 6/7 .

Find the number. Express your answer as a fraction in simplest form.

Answer 1

(1/7)x + (1/3)x = 6/7

 

 

Find the LCD of the equation.   LCD is 21.

 

(3x + 7x) / 21 = 18 / 21

 

 

Equate numerators.

 

3x + 7x = 18

 

10x = 18

 

   x = 1.8

 

 

Answer 2

Let x be the number you're trying to find.  Therefore:

 

1/7 x + 1/3 x = 6/7

 

Factor out x:

x (1/7 + 1/3) = 6/7

 

Find the least common denominator (21) and use that to add the fractions:

x (3/21 + 7/21) = 6/7

x (10/21) = 6/7

 

Divide both sides by 10/21:

x = (6/7) / (10/21) = (6/7) * (21/10) = 6 * (3/10) = 18/10 = 9/5