SOLUTION: John is presently 12 years older than Joseph. Four years ago John was twice as old as Joseph. How old is each now?

Algebra ->  Linear-equations -> SOLUTION: John is presently 12 years older than Joseph. Four years ago John was twice as old as Joseph. How old is each now?      Log On


   

Question 565508: John is presently 12 years older than Joseph. Four years ago John was twice as old as Joseph. How old is each now?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Joseph's age now
Let +b+ = John's age now
given:
(1) +b+=+a+%2B+12+
(2) +b+-+4+=+2%2A%28+a+-+4+%29+
-------------------
(2) +b+-+4+=+2a+-+8+
(2) +b+=+2a+-+8+%2B+4+
(2) +b+=+2a+-+4+
Substitute (1) into (2)
(2) +a+%2B+12+=+2a+-+4+
Subtract a from both sides
(2) +12+=+a+-+4+
Add +4+ to both sides
(2) +a+=+16+
and, since
(1) +b+=+a+%2B+12+
(1) +b+=+16+%2B+12+
(1) +b+=+28+
Joseph is 16 and John is 28
check:
(2) +b+-+4+=+2%2A%28+a+-+4+%29+
(2) +28+-+4+=+2%2A%28+16+-+4+%29+
(2) +24+=+2%2A12+
(2) +24+=+24+
OK