SOLUTION: In a box, there was a total of 2 353 blue and black marbles. Oliver took 3/7 of the blue marbles and 455 of the black marbles. After that, the number of blue marbles left was 2/3

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: In a box, there was a total of 2 353 blue and black marbles. Oliver took 3/7 of the blue marbles and 455 of the black marbles. After that, the number of blue marbles left was 2/3       Log On


   

Question 1185209: In a box, there was a total of 2 353 blue and black marbles. Oliver took 3/7 of the blue
marbles and 455 of the black marbles. After that, the number of blue marbles left was 2/3
the number of black marbles left. How many black marbles were there in the box at first?

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
In a box, there was a total of 2 353 blue and black marbles. Oliver took 3/7 of the blue
marbles and 455 of the black marbles. After that, the number of blue marbles left was 2/3
the number of black marbles left. How many black marbles were there in the box at first?
~~~~~~~~~~~~~~~ 

Let x be the number of black marbles, at first.

Then the number of the blue marbles was  (2353-x).


After removong,  4/7  of the blue marbles left and  (x-455)  black marbles left.


From the problem, we have this equation


    %284%2F7%29%2A%282353-x%29 = %282%2F3%29%2A%28x-455%29.


To solve it, multiply both sides by 21 and simplify


    12*(2353-x) = 14*(x-455)

    12*2353 - 12x = 14x - 14*455

    12*2353 + 14*455 = 14x + 12x

          34606      =     26x 

         x    = 34606%2F26 = 1331.


ANSWER.  There were 1331 black marbles in the box at first.

Solved.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The response from tutor @ikleyn shows a straightforward setup and solution for the problem.

I decided to just try a very different setup to see if the path to the solution was any easier....

After Oliver took 3/7 of the blue marbles, 4/7 of them were left; those 4/7 of the blue marbles were 2/3 of the number of black marbles left.

To use "nice" numbers, then, let the number of blue marbles left after Oliver took some be 4x; then the number of black marbles left was 6x. So

4x = blue marbles left
6x = black marbles left

Then

7x = blue marbles originally
6x+455 = black marbles originally

The total number of marbles originally was 2353:

7x%2B6x%2B455=2353
13x=1898
x=1898%2F13=146

ANSWERS: The numbers of marbles in the box originally were
blue: 7x = 7(146) = 1022
black: 6x+455 = 6(146)+455 = 1331

The algebra ended up being easier than with the solution shown by the other tutor; but it took more time to figure out how to set the problem up....

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The point of my response:

Never be afraid of looking at different ways of doing things -- that's how progress is made.

(If we never looked for better ways to do things, we would still all be living in caves....)