SOLUTION: Hi Darren and lynnette had $510 altogether. When lynette donated $46 to charity and Darren gave 1/9 of his money to lynnette both had an equal amount of money. How much did Darren

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Question 1199391: Hi
Darren and lynnette had $510 altogether. When lynette donated $46 to charity and Darren gave 1/9 of his money to lynnette both had an equal amount of money. How much did Darren have at first.
Thanks
Answer by ikleyn(52860) About Me  (Show Source):
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Darren and Lynnette had $510 altogether. When Lynette donated $46 to charity
and Darren gave 1/9 of his money to Lynnette both had an equal amount of money.
How much did Darren have at first.
~~~~~~~~~~~~~~~~~ 

Let D be the amount of money that Darren  had originally;

Then the amount of money that Lynnette had originally was  (510-D)  dollars.


After donating and giving, Linnette had  (510-D-46 + (1/9)*D)  dollars;  
Darren had  %288%2F9%29%2AD  dollars,  and we have equation

    510 - D - 46 + %281%2F9%29%2AD = %288%2F9%29%2AD,   (1)

or, equivalently,

    464 - D + %281%2F9%29%2AD = %288%2F9%29%2AD,   (1)


To solve this equation, multiplying both sides by 9

    464*9 - 8D = 8D.             (3)


Simplify and find D

    464*9 = 8D + 8D

    464*9 =   16D

      D   =  %28464%2A9%29%2F16 = 261.


ANSWER.  Originally, Darren had 261 dollars.

Solved.