One fifth of the sum of a number and 2 equals one third of the number. What is the number?

Question

One fifth of the sum of a number and 2 equals one third of the number. What is the number? Solve using fractional equations.

Answer 1

Let X be the number 

 

(1/5)*(X + 2) = (1/3)*X

(1/5)*X + 2/5 = (1/3)*X

(1/5)*X - (1/3)*X = -2/5

(3/15)*X - (5/15)*X = -2/5

-(2/15)*X = -2/5

X = (-2/5) / (-2/15) = (-2/5)*(15/(-2)) = 15/5 = 3

 

The number is 3

 

Check:  The sum of 3 and 2 is 5.  One fifth of 5 is 1.  One third of 3 is also 1.