SOLUTION: Justin and Darren had $1200 at first. Justin spent $400 while Darren spent $120 less than him. The amount Darren had left was 3/5 of the amount Justin had left. How much did Just

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Justin and Darren had $1200 at first. Justin spent $400 while Darren spent $120 less than him. The amount Darren had left was 3/5 of the amount Justin had left. How much did Just      Log On


   

Question 1184144: Justin and Darren had $1200 at first. Justin spent $400 while Darren
spent $120 less than him. The amount Darren had left was 3/5 of the
amount Justin had left. How much did Justin have at first?
Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
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Justin and Darren had $1200 at first. Justin spent $400 while Darren
spent $120 less than him. The amount Darren had left was 3/5 of the
amount Justin had left. How much did Justin have at first?
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Let x be the amount Justin had at first.

Then the amount Darren had at first was 1200-x dollars.



Justin spent 400 dollars; hence, his remainder is (x-400) dollars.

Darren spent (400-120) = 280 dollars;  hence, his remainder is  ((1200-x) - 280) = 920-x  dollars.



Next, the conditions says

    Darren_remainder%2FJustin_remainder = 3%2F5,

or

    %28920-x%29%2F%28x-400%29 = 3%2F5.



Cross multiply, simplify and find x


    5*(920-x) = 3*(x-400),

    4600 - 5x = 3x - 1200

    4600 + 1200 = 3x + 5x

       5800     = 8x

         x      = 5800/8 = 725.



ANSWER.  Justin had $725 at first.

Solved.