Question

Three merchants find a purse lying in the road. The first asserts that the discovery would make him twice as wealthy as the other two combined. The second claims his wealth would triple if he kept the purse, and the third claims his wealth would increase five fold.Let ?? represent the amount of money in the purse. Let ??,??, and ?? represents the amounts that are held by the first, second, and third merchants respectively.a. Write a system of equations that represents the problems.b. Suppose the amount in the purse is $20, how much does each of the merchants have before they find the purse?

Answer 1

Answer: the system of equation would be :

• A + Y = 2 (B+C)

• B + Y = 3B

• C + Y = 5C

the three merchants would have 10 dollars, 10 dollars, and 5 dollars respectively

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

1. 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:

• A + Y = 2 (B+C)

• B + Y = 3B

• C + Y = 5C

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