Answer: the system of equation would be :
the three merchants would have 10 dollars, 10 dollars, and 5 dollars respectively
Step-by-step explanation:
before finding the purse, lets assume the wealth of the 3 merchants were as follows:
first merchant = A dollars
second merchant = B dollars
third merchant = C dollars
- lets assume the purse contained Y dollars
After finding the purse they all claimed they would have the following:
first merchant said adding the money in the purse to his wealth would make him twice as rich as the other two combined : A + Y = 2 (B+C)
second merchant said adding the money in the purse to his wealth would make his wealth triple : B + Y = 3B
third merchant said adding the money in the purse to his wealth would make his wealth increase five folds : C + Y = 5C
third merchant = C dollars
therefore the system of equations to represent the problems are:
2. now when the money in the purse is 20 dollars (Y= 20 dollars ), from the equations above
the second merchant will have :
B + Y = 3B
B + 20 = 3B
3B - B = 20
2B = 20
B = 10 dollars
the third merchant will have :
C + Y = 5C
C + 20 = 5C
5C - C = 20
4C = 20
C = 5 dollars
the first merchant will have :
A + Y = 2 (B+C)
A + 20 = 2 ( 10 + 5)
A = 2 (15) - 20
A = 30 - 20
A = 10 dollars
