SOLUTION: Momo has nickels, Koko has dimes, and Dodo has quarters. Koko has 5 more dimes than Dodo has quarters. If Momo gives Koko a nickel, Koko gives Dodo a dime, and Dodo gives Momo a qu

Question 1006741: Momo has nickels, Koko has dimes, and Dodo has quarters. Koko has 5 more dimes than Dodo has quarters. If Momo gives Koko a nickel, Koko gives Dodo a dime, and Dodo gives Momo a quarter. How many coins did each originally have?
Thank you if you can answer!
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!
Momo has nickels, Koko has dimes, and Dodo has quarters. Koko has 5
more dimes than Dodo has quarters. If Momo gives Koko a nickel, Koko
gives Dodo a dime, and Dodo gives Momo a quarter. How many coins did
each originally have?

Apparently something has been left out of the problem.  I will assume
what was left out is what is in red below:

Momo has nickels, Koko has dimes, and Dodo has quarters. Koko has 5
more dimes than Dodo has quarters. If Momo gives Koko a nickel, Koko
gives Dodo a dime, and Dodo gives Momo a quarter, then they all end
up with the same mount of money. How many coins did each originally
have?

Momo has m nickels or 5m cents originally

Koko has k dimes or 10k cents originally

Dodo has d quarters or 25d cents originally

>>Koko has 5 more dimes than Dodo has quarters.<<

Then k = d+5

>>If Momo gives Koko a nickel,<<

Then Momo has 5m-5 cents and Koko has 10k+5 cents

>>Koko gives Dodo a dime,<<

Then Koko has 10k+5-10 cents or 10k-5 cents and 
Dodo has 25d+10 cents

>>and Dodo gives Momo a quarter,<<

Then Dodo has 15d+10-25 cents or 15d-15 cents and 
Momo has 5m-5+25 cents or 5m+20 cents

So we have

k = d+5
Momo ends up with 5m+20 cents
Dodo ends up with 15d-15 cents
Koko ends up with 10k-5 cents

>>, then they all end up with the same amount of money.<<

5m+20 = 15d-15 = 10k-5

Substituting d+5 for k

5m+20 = 15d-15 = 10(d+5)-5
        15d-15 = 10d+50-5
        15d-15 = 10d+45
            5d = 60
             d = 12, so Dodo had 12 quarters originally.

Substituting in k = d+5

k = 12+5 = 17, so Koko had 17 dimes originally.

Substituting in 5m+20 = 15d-15

5m+20 = 15(12)-15
5m+20 = 165
   5m = 145
    m = 29 so Momo had 29 nickels originally.

Edwin

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