SOLUTION: Euclid is supposed to have given the following problem (about 300 BC): A mule and a donkey were going to market laden with wheat. the mule said, "If you give me one measure, I sho

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Euclid is supposed to have given the following problem (about 300 BC): A mule and a donkey were going to market laden with wheat. the mule said, "If you give me one measure, I sho      Log On


   

Question 951600: Euclid is supposed to have given the following problem (about 300 BC):
A mule and a donkey were going to market laden with wheat. the mule said, "If you give me one measure, I should carry twice as much as you, but if I give you one, we should have equal burdens." what was each of their burdens?
Found 2 solutions by josmiceli, macston:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +m+ = mule's burden
Let +d+ = donkey's burden
--------------------------
given:
(1) +m+%2B+1+=+2%2A%28+d+-+1+%29+
(2) +m+-+1++=+d+%2B+1+
------------------------
(1) +m+%2B1++=+2d+-+2+
(1 +2d+-+m+=+3+
and
(2) +m+-+1++=+d+%2B+1+
(2) +-d+%2B+m+=+2+
--------------------
Add (1) and (2)
+d+=+5+
and
(1) +m+%2B+1+=+2%2A%28+d+-+1+%29+
(1) +m+%2B+1+=+2%2A%28+5+-+1+%29+
(1) +m+=+2%2A4+-+1+
(1) +m+=+7+
The mule has 7 and the donkey has 5
---------------------------------
check:
Donkey gives mule 1, so donkey now
has 4 and mule has 8
8 is twice 4, OK
------------------
Mule gives donkey 1, so mule has 6 and
donkey has 6
6 = 6, OK


Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
m=mule's load; d=donkey's load
m-1=d+1 Add 1 to each side.
m=d+2
m+1=2(d-1) Substitute for m.
d+2+1=2d-2 Add 2 to each side.
d+5=2d Subtract d from each side.
5=d ANSWER 1:The donkey carries 5 measures.
m=d+2=5+2=7 ANSWER 2: The mule carries 7 measures.
CHECK:
m+1=2(d-1)
7+1=2(5-1)
8=2(4)
8=8