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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