SOLUTION: Please help me with this question. A pony and a donkey were carrying some bundles of cloth for a cloth merchant. On the way, the donkey said to the pony, "If I give you one bundl

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Please help me with this question. A pony and a donkey were carrying some bundles of cloth for a cloth merchant. On the way, the donkey said to the pony, "If I give you one bundl      Log On


   

Question 625065: Please help me with this question.
A pony and a donkey were carrying some bundles of cloth for a cloth merchant. On the way, the donkey said to the pony, "If I give you one bundle, my load will be half of yours." In an angry mood, the pony retorted, "Why don't you take one bundle from me, then my load will be half of yours!" Assuming that the bundles are of equal weight, how many bundles did the pony and the donkey each carry?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +p+ = the number of bundles the pony carries
Let +d+ = the number of bundles the donkey carries
given:
(1) +%281%2F2%29%2A%28+p+%2B+1+%29+=+d+-+1+
and
(2) +%281%2F2%29%2A%28+d+%2B+1+%29+=+p+-+1+
-------------------
(1) +p+%2B+1+=+2%2A%28+d+-+1+%29+
(1) +p+%2B+1+=+2d+-+2+
(1) +2d+-+p+=+3+
and
(2) +%281%2F2%29%2A%28+d+%2B+1+%29+=+p+-+1+
(2) +d+%2B+1+=+2%2A%28+p+-+1+%29+
(2) +d+%2B+1+=+2p+-+2+
(2) +d+-+2p+=+-3+
Multiply both sides of (2) by +2+
and subtract (2) from (1)
(1) +2d+-+p+=+3+
(2) +-2d+%2B+4p+=+6+
+3p+=+9+
+p+=+3+
and
(2) +d+-+2p+=+-3+
(2) +d+-+2%2A3+=+-3+
(2) +d+=+6+-+3+
(2) +d+=+3+
They each have 3 bundles
check:
(1) +%281%2F2%29%2A%28+p+%2B+1+%29+=+d+-+1+
(1) +%281%2F2%29%2A%28+3+%2B+1+%29+=+3+-+1+
(1) +4%2F2+=+2+
(1) +2+=+2+
and
(2) +%281%2F2%29%2A%28+d+%2B+1+%29+=+p+-+1+
(2) +%281%2F2%29%2A%28+3+%2B+1+%29+=+3+-+1+
(2) +4%2F2+=+2+
(20 +2+=+2+
OK