SOLUTION: A CLIMBER ASCENDS 500 FT ON THE 1ST HOUR. AND 10 FT LESS IN EACH SUCCEEDING HOURS WHEN WILL HE BE 3720 ABOVE HIS STARTING POINT

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A CLIMBER ASCENDS 500 FT ON THE 1ST HOUR. AND 10 FT LESS IN EACH SUCCEEDING HOURS WHEN WILL HE BE 3720 ABOVE HIS STARTING POINT      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 949915: A CLIMBER ASCENDS 500 FT ON THE 1ST HOUR. AND 10 FT LESS IN EACH SUCCEEDING HOURS WHEN WILL HE BE 3720 ABOVE HIS STARTING POINT
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let n = number of hours passed
You are summing:
+500+-+10n+ for n = 1,2,3,4, ...
This numerical sequence = +n%2A%28+n%2B1+%29%2F2+
For instance, say +n+=+5+
+1+%2B+2+%2B+3+%2B+4+%2B+5+=+5%2A6%2F2+
check it -it works
---------------------
Now I can say:
+3720+=+500n+-+10%2A%28n%2A%28n%2B1%29%2F2%29+
+7440+=+1000n+-+10%2A%28+n%5E2+%2B+n+%29+
+10n%5E2+%2B+10n+-+1000n+%2B+7440+=+0+
+10n%5E2+-+990n+%2B+7440+=+0+
+n%5E2+-+99n+%2B+744+=+0+
+n+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+-99+
+c+=+744+
+n+=+%28-%28-99%29+%2B-+sqrt%28+%28-99%29%5E2-4%2A1%2A744+%29%29%2F%282%2A1%29+
+n+=+%28+99+%2B-+sqrt%28+9801+-+2976+%29%29%2F+2+
+n+=+%28+99+%2B-+sqrt%28+6825+%29%29%2F+2+
+n+=+%28+99+-+82.6%29%2F+2+ ( makes sense to use -sqrt )
+n+=+%28+99+-+83+%29%2F2+ ( rounded off 82.6 )
+n+=+16%2F2+
+n+=+8+
check:
+500+%2B+490+%2B+480+%2B+470+%2B+460+%2B+450+%2B+440+%2B+430+=+3720+
OK