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(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
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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.
