Question

Three generous friends, each with some cash, redistribute their money as follows: Ami gives enough money to Jan and Toy to double the amount that each has. Jan then gives enough to Ami and Toy to double their amounts. Finally, Toy gives Ami and Jan enough to double their amounts. If Toy has $\$36$ when they begin and $\$36$ when they end, what is the total amount that all three friends have?

$\$108$

$\$180$

$\$216$

$\$252$

$\$288$

Solution:

Toy begins with $\$36$ . After Ami doubles Toy's amount, Toy has $\$72$ . After Jan doubles Toy's amount, Toy has $\$144$ .

On Toy's final turn, Toy ends with $\$36$ , so Toy gives away $\$144-\$36=\$108$ . That gift doubles the combined amount of Ami and Jan, so Ami and Jan together had $\$108$ just before Toy's final turn.

The total amount of money is constant, so the total is $\$144+\$108=\$252$ .

Thus, the correct answer is D .

1998 AMC 8 Problem 25

Solution:

Problem 25 in Other Years