Subj:.....Annual
Picnic (S627)
From the book
"Mathematical Puzzles of Sam Loyd"
Edited by Martin Gardner
From: Dover Publications in 1959 

Photo from BakerRanchLava.com 
.
When they started
off on the great annual picnic, every
wagon carried exactly
the same number of persons. Half
way to the grounds
ten wagons broke down, so it was
necessary for each
remaining wagon to carry one more
person.
When they started
for home it was discovered that
fifteen more wagons
were out of commission, so on the
return trip there
were three persons more in each wagon
than when they started
out in the morning. How many
people attended the
great annual picnic?
.
.
.


Finger pointing down
from darrell94590 on 1/2/2006 
.
.
THE SOLUTION
Let N = the number
of people originally in each wagon
and W = the number
of wagons originally going to the picnic.
The equation for going
to the picnic is
W N = ( N + 1 ) (
W  10 )
and the equation for
returning from the picnic is
W N = ( N + 3) ( W
 25 )
Using
elementary Algebra
to solve two equations
with two unknowns
yields
N = 9 and W = 100.
Therefore there were
900 people
at the annual picnic. 

Photo from
BakerRanchLava.com 
