Natalie has some nickles, Dirk has some dimes, and Quincy has some quarters. Dirk has five more dimes than Quincy has quarters. If Natalie gives Dirk a nickel, Dirk gives Quincy a dime, and Quincy gives Natalie a quarter, they will all have the same amount of money. How many coins did each have originally?

Answer 1

Quincy --- x quarters
Dirk ------ x+5 dimes
Natalie ---- y nickles

after giveaway:
Quincy ---- 1 dime + x-1 quarters
Dirk ---- 1 nickel + x+4 dimes
Natalie --- (y-1) nickels + 1 quarter

10 + 25(x-1) = 5 + 10(x+4) = 25 + 5(y-1)

10 + 25(x-1) = 5 + 10(x+4)
10 + 25x - 25 = 5 + 10x + 40
15x = 60
x = 4

5 + 10(x+4) = 25 + 5(y-1)
5 + 10x + 40 = 25 + 5y - 5
45 + 10(4) = 20 + 5y
65 = 5y
y = 13

Quincy had 4 quarters
Dirks had 9 dimes
Natalie had 13 nickels

check:
after giveaway
Quincy has 1 dime + 3 quarters ---> 85 cents
Dirk has 1 nickel + 8 dimes ---- > 85 cents
Natalie has 12 nickels + 1 quarter ---> 85 cents
YEAH!!!!