how do i complete this word problem?

Question

tim kate and raymond are comparing their ages. The sum of their ages is 50. tim is 3 times older than raymond. kate is 5 years older than raymond. what are their ages?

Answer 1

Let tim's age is x,raymond's age is y and kate's age is z then

 

x+y+z=50 ....Eq1

 

Also, we have

x=3y

z=y+5

 

put these values in Eq1

 

(3y)+y+(y+5)=50

∴5y+5=50

∴5y=45

∴y=45/5

∴y=9

 

∴x=3*9=27

 

and z=y+5

        =9+5

∴z=14

 

so we have:

 

tim's age is 27 years, Kate's age is 14 years and raymond's age is 9 years. ...  Ans

 

Lets check if we are right.

 

27+14+9=50