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

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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.

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