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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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- Age problems and their solutions
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- Age problems for mental solution
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The referred lessons are the part of this online textbook under the topic "Age word problems".
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