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Sagot :
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.
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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