Multiple choice

William, Michael and Samuel divide some money such that if William gives some of his money to Michael, then Michael and Samuel will have equal amount of money. Instead, if Samuel gives the same amount to William, William will have twice the amount of money that Michael has. If William and Michael have money in the ratio 3 : 2, what percentage of the total money did Michael get?

  1. 20%

  2. 25%

  3. 33.33%

  4. 40%

  5. 50%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let W=3x, M=2x. Total = 5x+S. The problem describes a system of linear equations based on the transfers. Solving for the proportions shows Michael gets 25% of the total.

AI explanation

Let the total money be T, the amount transferred be x, and let William and Michael have 3y and 2y. If William gives x to Michael, Michael's amount becomes 2y + x, which must equal Samuel's amount of T - 5y. If Samuel gives x to William, William's amount becomes 3y + x, which equals twice Michael's amount of 4y, giving x = y. Substituting y for x reveals Samuel's amount is 3y, and since William and Michael have 3y and 2y, the ratio of their amounts to the total is 3 : 2 : 3. Michael's fraction of the total is 2 / (3 + 2 + 3) = 2/8 = 1/4, which equals 25%.

Keep practicing — related questions