**Carlos = C**

**Ramon = R**

**Jun = J**

Carlos is half as old as Ramon

R/2 = C **1st equation**

Jun is 11 years older than Carlos

C + 11 = J **2nd equation**** ****no. 1**

Therefore;

J = R/2 + 11 **2nd equation no. 2**

Half of Ramon's age four years from now will be 9 years less than the sum of half Jun's age four years from now and Carlos' present age.

(R + 4)/2= ((J + 4)/2 + C) - 9 **main equation**

Let's now substitute the value of C and J to the main equation.

(R + 4)/2= (((R/2 + 11) + 4 + R/2)/2) - 9

Add 11 and 4

(R + 4)/2= ((R/2 + 15 + R/2)/2) - 9

Multiply both sides by 2

(R + 4)/2 * 2 = (((R/2 + 15 + R/2)/2) - 9) * 2

R + 4 = R/2 + 15 + R/2 - 18

Add the two R/2; Subtract 15 and 18

R + 4 = 2R/2 - 3

Multiply both sides by 2

(R + 4) * 2 = (2R/2 - 3) * 2

R + 8 = 2R - 6

Transpose 8 and 2R

R - 2R = -6 - 8

-R = -14

Multiply both by -1

Therefore;

**(R)amon's age is 14**

Let's now substitute the value of R to the 1st equation

14/2 = C

Therefore;

**(C)arlos' age is 7**

Now substitute the value of C to the 2nd equation no. 1

7 + 11 = J

Therefore;

**(J)un's age is 18**

Let us now check by substituting all f the value in the main equation

(14 + 4)/2= ((18 + 4)/2 + 7) - 9

Add all in parenthesis

18/2 = (22/2 + 7) - 9

Divide

9 = (11 + 7) - 9

Add

9 = 18 - 9

Subtract

**9 = 9 Correct**

I hope i made it clear to you.

I hope this helps.