SOLUTION: Nadine has seven more nickels than Delano has dimes. If Delano gives Nadine four of his dimes, Delano will have the same amount of money as Nadine. How much money do they have t

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Question 108061: Nadine has seven more nickels than Delano has dimes. If Delano gives Nadine four of his dimes, Delano will have the same amount of money as Nadine. How
much money do they have together? (Assume that Nadine has only nickels and Delano has only dimes.)
Thank you.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Let's say that Nadine has n nickels and Delano has d dimes.

So we know a couple of things:

1) n+=+d+%2B+7: Because Nadine has 7 more nickels than Delano has dimes
:
2) Nadine has 5n cents total
:
3) Delano has 10d cents total
:
4) But if Delano gives Nadine 40 cents, then the amount of money they both have will be the same:
:
5n%2B40=10d-40: Plus 40 on the left, because Nadine's money increased, and minus 40 on the right because Delano's money decreased.
:
5%28d%2B7%29%2B40=10d-40: substituting d+7 for n
5d%2B35%2B40=10d-40: distribute
5d-10d=-40-40-35: collect terms
-5d=-115: simplify
d+=+23: divide by -5
:
Now we know that Delano had 23 dimes to start. Therefore Nadine must have had 23 + 7 or 30 nickels.
:
Let's check the answer:
:
Delano started with 23 * 10 cents = 230 cents or $2.30.
:
Nadine started with 30 * 5 cents = 150 cents or $1.50.
:
If Delano gives 4 dimes to Nadine, then Nadine will have $1.90, and Delano will have $1.90. Check!