SOLUTION: Ben is seven more than two times as old as Henry. In 13 years the sum of their ages will be 78. How old is Ben now?

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: Ben is seven more than two times as old as Henry. In 13 years the sum of their ages will be 78. How old is Ben now?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 721268: Ben is seven more than two times as old as Henry. In 13 years the sum of their ages will be 78. How old is Ben now?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +b+ = Ben's age now
Let +h+ = Henry's age now
+b+%2B+13+ = Ben's age in 13 yrs
+h+%2B+13+ = Henry's age in 13 yrs
given:
(1) +b+=+2h+%2B+7+
(2) +%28+b+%2B+13+%29+%2B+%28+h+%2B+13+%29+=+78+
-------------------------------
(2) +b+%2B+h+%2B+26+=+78+
(2) +b+%2B+h+=+52+
and
(1) +b+-+2h+=+7+
----------------
Subtract (1) from (2)
(2) +b+%2B+h+=+52+
(1) +-b+%2B+2h+=+-7+
+3h+=+45+
+h+=+15+
and, since
(1) +b+=+2h+%2B+7+
(1) +b+=+2%2A15+%2B+7+
(1) +b+=+37+
-------------
Ben is 37 now
check answer:
(2) +%28+b+%2B+13+%29+%2B+%28+h+%2B+13+%29+=+78+
(2) +%28+37+%2B+13+%29+%2B+%28+15+%2B+13+%29+=+78+
(2) +50+%2B+28+=+78+
(2) +78+=+78+
OK