SOLUTION: Hi The number of marbles in box A is half the number in box B. All the marbles in box A are black. Box B contains black and white marbles. In box B the number of black marbles is

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Question 1209492: Hi
The number of marbles in box A is half the number in box B. All the marbles in box A are black. Box B contains black and white marbles. In box B the number of black marbles is 3/4 the number of white marbles. There are 28 more black marbles in box A than in box B. What is the number of marbles in box A and box B


Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
.
(a) The number of marbles in box A is half the number in box B.
(b) All the marbles in box A are black.
(c) Box B contains black and white marbles.
(d) In box B the number of black marbles is 3/4 the number of white marbles.
(e) There are 28 more black marbles in box A than in box B.
What is the number of marbles in box A and box B
~~~~~~~~~~~~~~~~~~~~~~~~~~


        I marked all conditions by letters for easy referring.

Let x be the number of all marbles in box A.  (They all are black.)

In box B we have 3y black marbles and 4y white marbles,
   where y is some integer positive number (the common measure).


From condition (a), we have this equation

    2x = 3y + 4y,  or  2x = 7y.    (1)


From condition (e), we have this equation

    x - 3y = 28.                   (2)


To solve, from equation (2) express x = 28 + 3y  and substitute it into equation (1).  You will get

    2(28+3y) = 7y.


Simplify and find y

    56 + 6y = 7y

    56 = 7y - 6y.

    56 = y.


So, the number of all marbles in box B is 7y = 7*56 = 392.

    The number of all marbles in box A is half of that, i.e.  392/2 = 196.


From the problem's question, I can not get, if they want the total number of marbles or separate numbers.


In my view, the question is worded in extremely illiterate/inaccurate  form; 
in the true Math problems, professional composers NEVER write it in this way.


True question must ask either 

    "What is the number of marbles in box A and box B separately ?"

or

    "What is the total number of marbles in box A and box B ?".


But as I see it in many incoming posts, the major goal of the local problem composers
is to confuse a reader.


If you need the total, then add 392 and 196:  392 + 196 = 588.

Solved.



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