Natalie has some nickels, 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?

Kendra Hudson

Kendra Hudson

Answered question

2022-09-05

Natalie has some nickels, 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 & Explanation

Hajdiniax

Hajdiniax

Beginner2022-09-06Added 8 answers

natalie x nickels
dirk y dimes
quincy z quarters
Dirk has five more dimes than Quincy has quarters y =z+5
If Natalie gives Dirk a nickel, Dirk gives Quincy a dime,andQuincy gives Natalie a quarter, thye will all have the same amount of money
5x-5+25=10y+5-10=25z+10-25
5x +20 = 10y-5 =25z-15
we know that y = z+5
so
10(z+5) - 5 = 25z - 15
10z+45 = 25z - 15
60 = 15z
z= quincy = 4 coins
y=z+5 = dirk = 9 coins
and 5x +20 = 10y-5 >> 5x +20 = 90-5 >>. 5x =65>> x=natalie=13

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