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
