Four brothers have together forty-eight Kwanzas. If the first brother's money were increased by three Kwanzas, if the second brother's money were decreased by three Kwanzas, if the third brother's money were triplicated and if the last brother's money were reduced by a third, then all brothers would have the same quantity of money. How much money does each brother have?
Solution
Let and be the amounts of money that the first, second, third, and fourth brothers have, respectively. According to the problem, we have the following equation describing their total amount of money:
We are also given conditions on how these amounts are adjusted:
1. The first brother's money is increased by 3 Kwanzas: .
2. The second brother's money is decreased by 3 Kwanzas: .
3. The third brother's money is tripled: .
4. The fourth brother's money is reduced by a third: .
These adjustments result in all brothers having the same amount of money. Let's denote this common amount by . Therefore, we have the following equations:
Solving these equations for in terms of each brother's amount, we get:
Substituting these into the total money equation:
Simplifying:
Combine terms:
Multiply the entire equation by 3 to eliminate the fraction:
Solving for :
Now, substitute back into the expressions for and :
Thus, the amounts of money each brother has are: