word problems

Question

If the same number is added to the numerator and denominator of 2/5,the resulting fraction is equal to 2/3. What is the number?

Answer 1

let n = the number

 

(2 + n)/(5 + n) = 2/3

 

I'll attempt to write it in this form so you can see the process of cross-multiplication

 

   2 + n       2

  -------   = ---

   5 + n       3

 

Cross multiply

 

3(2 + n) = 2(5 + n)

 

6 + 3n = 10 + 2n

  

3n = 4 + 2n

 

n = 4  This is the number

 

to check :

 

 2 + 4         2

--------  =  ---

 5 + 4         3

 

 6      2

--- = ---    Yes it checks

 9      3