SOLUTION: Ted is 12 years older than Juan. Next year ted will be 3 times as old as Juan. How old is Juan?

Question 1123149: Ted is 12 years older than Juan. Next year ted will be 3 times as old as Juan. How old is Juan?
Found 2 solutions by ikleyn, ankor@dixie-net.com:
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
Formal solution

T = J + 12 (1) ("Ted is 12 years older than Juan.") T + 1 = 3*(J+1) (2) ("Next year ted will be 3 times as old as Juan.") From eq(1), substitute the expression for T into eq(2), replacing T. You will get (J + 12) + 1 = 3*(J+1), J + 13 = 3J + 3 13 - 3 = 3J - J 10 = 2J ====> J = 10/2 = 5. Answer. Juan is 5 years old. Check. Ted is 5+12 = 17 years old. Next year Juan will be 6 years old; Ted will be 18 years old, i.e. three times Juan's age then. ! Correct !

Logic solution

Next your Ted will be 3 times Juan's age and 12 years older than Juan. Hence (apply your logic skills !), Tedd will be 18, while Juan will be 6. It means that Juan is 5 years old now, while Ted is 17 years old.

Solved by two different ways giving the same result.

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Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
Ted is 12 years older than Juan.
t = j + 12
Next year ted will be 3 times as old as Juan.
t + 1 = 3(j+1)
t = 3j + 3 -1
t = 3j + 2
replace t with (j+12)
j + 12 = 3j + 2
j - 3j = 2 - 12
-2j = -10
j = -10/-2
j = 5 yrs is Juan?
:
:
Check this find Ted's age, 12 + 5 = 17
check this in the statement
"Next year ted will be 3 times as old as Juan. "
17 + 1 = 3(5 + 1)
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