SOLUTION: A teacher is four times as old as a student. In 12 years, the student’s age will be half of the teacher’s age. How old are they now?

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Question 1116901: A teacher is four times as old as a student. In 12 years, the student’s age will be half of the teacher’s age. How old are they now?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the teacher's age now
Let +b+ = the student's age now
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(1) +a+=+4b+
(2) +b+%2B+12+=+%281%2F2%29%2A%28+a+%2B+12+%29+
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(2) +2b+%2B+24+=+a+%2B+12+
Plug (1) into (2)
(2) +2b+%2B+24+=+4b+%2B+12+
(2) +2b+=+12+
(2) +b+=+6+
and
(1) +a+=+4b+
(1) +a+=+4%2A6+
(1) +a+=+24+
The teacher is 24
The student is 6
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check:
(2) +b+%2B+12+=+%281%2F2%29%2A%28+a+%2B+12+%29+
(2) +6+%2B+12+=+%281%2F2%29%2A%28+24+%2B+12+%29+
(2) +18+=+%281%2F2%29%2A36+
(2) +18+=+18+
OK