SOLUTION: Gary is as old as Harry will be when Gary is twice as old as Harry was when Gary’s age was half the sum of their present ages. Harry is as old as Gary was when Harry was half t

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: Gary is as old as Harry will be when Gary is twice as old as Harry was when Gary’s age was half the sum of their present ages. Harry is as old as Gary was when Harry was half t      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1048832: Gary is as old as Harry will be when Gary is twice as old as Harry was when Gary’s age was half the sum of their present ages.
Harry is as old as Gary was when Harry was half the age he will be 10 years from now.
What is Harry’s age?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +g+ = Gary's age now
Let +h+ = Harry's age now
---------------------------
With these types of problems, I start at
the end of a statement.
----------------------------------
"when Gary’s age was half the sum of their present ages."
Gary's age was +%28+g+%2B+h+%29%2F2+
---------------------------------
"as Harry was when Gary’s age was half the sum of their present ages."
Harry was what was Gary's age then plus the difference in
their ages ( I'm assuming Harry is the older one )
--------------------------------------------
Harry's age was +%28+g+%2B+h+%29+%2F+2+%2B+%28+h+-+g+%29+
--------------------------------------------
"when Gary is twice as old as Harry was when Gary’s
age was half the sum of their present ages."
-----------------------------------------------
This is when Gary is:
+2%2A%28+%28+g%2Bh+%29%2F2+%2B+%28+h-g+%29+%29+
-----------------------------
"as Harry will be when Gary is twice as old as Harry was
when Gary’s age was half the sum of their present ages.
This means I have to add the difference in their ages again
------------------------------
Harry will be:
+2%2A%28+%28+g%2Bh+%29%2F2+%2B+%28+h-g+%29+%29+%2B+%28+h-g+%29+
------------------------------------
I am told that Gary is presently this age, so I can say:
(1) +g+=+2%2A%28+%28+g%2Bh+%29%2F2+%2B+%28+h-g+%29+%29+%2B+%28+h-g+%29+
------------------------------------------
Reading the 2nd statement:
"when Harry was half the age he will be 10 years from now."
Harry was:
+%281%2F2%29%2A%28+h+%2B+10+%29+
---------------------
"as Gary was when Harry was half
the age he will be 10 years from now."
-----------------------------------
Gary was the younger, so I will subtract the difference in their ages
+%281%2F2%29%2A%28+h+%2B+10+%29+-+%28+h-g+%29+
----------------------------
This is Harry's age now, so I can say:
(2) +h+=+%281%2F2%29%2A%28+h%2B10+%29+-+%28+h-g+%29+
----------------------------------
(1) +g+=+2%2A%28+%28+g%2Bh+%29%2F2+%2B+%28+h-g+%29+%29+%2B+%28+h-g+%29+
(1) +g+=+%28+g%2Bh+%29+%2B+2%2A%28+h+-+g+%29+%2B+%28+h-g+%29+
(1) +g+=+g+%2B+h+%2B+2h+-+2g+%2B+h+-+g+
(1) +g+=+-2g+%2B+4h+
(1) +3g+=+4h+
(1) +h+=+%283%2F4%29%2Ag+
( It seems that Harry was actually younger )
----------------------------------------
(2) +h+=+%281%2F2%29%2A%28+h%2B10+%29+-+%28+h-g+%29+
(2) +2h+=+h+%2B+10+-2%2A%28+h-g+%29+
(2) +h+=+10+-+2h+%2B+2g+
(2) +3h+=+2g+%2B+10+
(2) +2g+=+3h+-+10+
(2) +g+=+%283%2F2%29%2Ah+-+5+
-----------------------
By substitution:
(1) +h+=+%283%2F4%29%2A%28%28+3%2F2%29%2Ah+-+5+%29+
(1) +4h+=+3%2A%283%2F2%29%2Ah+-+20+
(1) +8h+=+9h+-+40+
(1) +h+=+40+
------------------
Harry is 40
------------------
check:
(2) +g+=+%283%2F2%29%2Ah+-+5+
(2) +g+=+%283%2F2%29%2A40+-+5+
(2) +g+=+60+-+5+
(2) +g+=+55+
-------------------------
You can go back to the start and try
to prove this step by step. I'm too
tired. Hope I got it right!
Get a 2nd opinion if you like.