SOLUTION: Three merchants find a purse lying in the road. One merchant says �If I keep the purse, 1 shall have twice as much money as the two of you together� �Give me the purse and I shall

Question 1130073: Three merchants find a purse lying in the road. One merchant says �If I keep the purse, 1 shall have twice as much money as the two of you together� �Give me the purse and I shall have three times as much as the two of you together� said the second merchant. The third merchant said �I shall be much better off than either of you if I keep the purse, I shall have five times as much as the two of you together.� If there are 60 coins (of equal value) in the purse, how much money does each merchant have?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Three merchants find a purse lying in the road. there are 60 coins (of equal value) in the purse,
a, b, c
write an equation for each statement, simplify as much as possible
One merchant says
�If I keep the purse, 1 shall have twice as much money as the two of you together�
a + 60 = 2(b+c)
a = 2b + 2c - 60
a - 2b - 2c = -60
�Give me the purse and I shall have three times as much as the two of you together� said the second merchant.
b + 60 = 3(a+c)
b = 3a + 3c - 60
-3a + b - 3c = -60
" The third merchant said �I shall be much better off than either of you if I keep the purse, I shall have five times as much as the two of you together.�
c + 60 = 5(a+b)
c = 5a + 5b - 60
-5a - 5b + c = -60
:
The easiest way is to use the 3 X 4 matrix feature on your calc and enter
1 -2 -2 -60
-3 1 -3 -60
-5 -5 1 - 60
from this we get the amt each merchant has:
a = 4
b = 12
c = 20
:
You can check this yourself in each statement.

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