SOLUTION: Aunt Alice gave each of her three nieces a number of silver dollars equal to their ages. The youngest felt that this was unfair. They agreed to redistribute the money. The youngest

Question 164470: Aunt Alice gave each of her three nieces a number of silver dollars equal to their ages. The youngest felt that this was unfair. They agreed to redistribute the money. The youngest would split half of her silver dollars evenly with the other two sisters. The middle would then give each of the others 4 silver dollars. Finally, the oldest was to split half of her dollars equally between the two younger sisters. After exchanging the money, each girl had 12 silver dollars. How old are the sisters? (Their ages = 36)
Answer by josmiceli(6784) (Show Source):
You can put this solution on YOUR website!
Let = youngest age
Let = middle one's age
Let = oldest one's age
The youngest would split half of her silver dollars evenly with the other two sisters.
The middle and oldest sisters get and silver dollars
The middle, who now has gives to the others
So, the middle now has
The youngest has
The oldest has
Now the oldest gives 1/2 her money to the other sisters
The oldest now has
Each sister gets
So, the middle one has
And, the youngest has
Now each girl has 12 silver dollars

(youngest)
middle
oldest
---------------------------
Multiply each equation by
(1)
(2)
(3)
---------------------------
Multiply (1) by , then subtract (3) from (1)
(1)
(3)

Substitute this in (3)
(3)

Substitute and in (2)
(2)

Their ages are 4,13 and 19