Question 108061
Let's say that Nadine has n nickels and Delano has d dimes.


So we know a couple of things:


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