Algebra HELP?

Question

Nadine has seven more nickels than Delano has dimes. If Delano gives Nadine four of his dimes, then Delano will have the same amount of money as Nadine. How much money do they have together? (Assume that Nadine only has nickels and Delano only has dimes.)

Use only one variable and show work

Answer 1

Okay, here it goes...

Delano has an amount of dimes n
Nadine has an amount of nickels equal to Delano's dime plus 7 or n + 7.

The amount of money each of them has can be represented this way.

Delano 10n
Nadine 5(n +7)

Now we've also been told that if Delano gives four of his dimes to Nadine that they will each have the same amount of money. If then happens then Delano will have an amount of money that is the equivalent of four dimes less that he had:

10(n-4)

And Nadine will have an amount of money equal to four dimes more than she had:

5(n + 7) + 40

40 being the amount of cents equal to 4 dimes

So therefore, we can create the equality:

5(n + 7) + 40 = 10(n -4) or by distributive multiplication

5n + 35 + 40 = 10n - 40 or by performing initial arithmetic operations

5n + 75 = 10n - 40 or by adding 40 to each side

5n + 115 = 10n or by subtracting 5n from each side

115 = 5n therefore, if we divide each side by 5

23 = n

To check this, Delano's 23 dimes would give him $2.30. Nadine would have 7 more nickels that Delano has dimes and so she would have a total of 30 nickels for a total of $1.50. If Delano gives her 4 dimes or $.40, her total will rise to $1.90 while his will fall from $2.30 to $1.90. The value checks.