SOLUTION: hi please try to solve this problem for me twelve years ago, gabriel was four times as old as grant. today, grant is eight years older than twice grant's age now. how old is gab

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: hi please try to solve this problem for me twelve years ago, gabriel was four times as old as grant. today, grant is eight years older than twice grant's age now. how old is gab      Log On

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Question 773087: hi please try to solve this problem for me
twelve years ago, gabriel was four times as old as grant. today, grant is eight years older than twice grant's age now. how old is gabriel now?
thanks so much

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Gabriel's age now
Let +b+ = Grant's age now
+a+-+12+ = Gabriel's age 12 yrs ago
+b+-+12+ = Grant's age 12 yrs ago
--------------------------------
(1) +a+-+12+=+4%2A%28+b+-+12+%29+
(2) +a+=+2b+%2B+8+
-----------------
Note that you mistyped:
"GRANT is eight years older than twice GRANT's age now"
It should be:
"Gabriel is eight years older than twice grant's age now"
------------------
(1) +a+-+12+=+4b+-48+
(1) +a+-+4b+=+-36+
and
(2) +a+-+2b+=+8+
-----------------
Subtract (1) from (2)
(2) +a+-+2b+=+8+
(1) +-a+%2B+4b+=+36+
+2b+=+44+
+b+=+22+
and, since
(2) +a+-+2b+=+8+
(2) +a+-+2%2A22+=+8+
(2) +a+=+44+%2B+8+
(2) +a+=+52+
Gabriel is 52 now
check:
(1) +a+-+12+=+4%2A%28+b+-+12+%29+
(1) +52+-+12+=+4%2A%28+22+-+12+%29+
(1) +40+=+4%2A10+
(1) +40+=+40+
Ok
(2) +a+=+2b+%2B+8+
(2) +52+=+2%2A22+%2B+8+
(2) +52+=+44+%2B+8+
(2) +52+=+52+
OK