Question 1029396: Three men, each having denarii, found a purse containing 23 denarii. The first
man said to the second, “If I take this purse, I will have twice as much as you.”
The second said to the third, “If I take this purse, I will have three times as much as you.” The third man said to the first, “If I take this purse, I will have four times as much as you.” How many denarii did each man have?
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! Call what the three men had, a, b, and c.
Then we can write
a + 23 = 2b
b + 23 = 3c
c + 23 = 4a
We will take three equations and three unknowns and boil it down to two equations and two unknowns...
The first one becomes
(1/2)a + 11.5 = b
Plug that in to the second and get
(1/2)a + 11.5 + 23 = 3c
(1/2)a + 34.5 = 3c
or
(1/2)a - 3c = -34.5
or
a - 6c = -69
Let's combine this with the 3rd equation
-4a + c = -23
-24a + 6c = -138
Now add them
a - 6c = -69
+(-24a + 6c = -138)
--------------------
-23a = -207
a = 9
giving us
b = 16
and
c = 13
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