Find the age of each?

Question

carlos is half as old as ramon while jun is 11 years older than carlos.if half ramon's age 4 years from now will be 9 years less than the sum of half of jun's age 4 years from now and carlos' present age, find the ages of each?

Answer 1

Let the ages be represented by the first letter of their names.

C=R/2; J=C+11; (R+4)/2=(J+4)/2+C-9. From these we have R=2C. Substitute for R and C in the third equation:

(2C+4)/2=(C+15)/2+C-9. This equation contains only one variable so should be solvable. Multiply through by 2:

2C+4=C+15+2C-18, C=7. So we can calculate R=2*C=14; and J=C+11=18. 

Check: Carlos is half as old as Ramon, C is half of 14; Ramon and Jun will be 18 and 22 in 4 years' time. Half of Jun's age then (11) plus Carlos' age now (7) is 18. Half of Ramon's age in 4 years will be 9 which is 9 less than this sum.

So the facts check out and Carlos is 7, Ramon is 14 and Jun is 18.