SOLUTION: There are two boxes of balls. The 1st box has 15 more than the 2nd box. All balls in the 2nd box are red. 2/5 of the first box are red balls. There are 69 red balls all together. H

Question 1163681: There are two boxes of balls. The 1st box has 15 more than the 2nd box. All balls in the 2nd box are red. 2/5 of the first box are red balls. There are 69 red balls all together. How many balls in total from the 2 boxes?
Answer by ikleyn(52908) (Show Source): You can put this solution on YOUR website!
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    0.4x + y = 69     (1)   (counting all red balls:  69 red balls altogether)

       x - y = 15     (2)   (The 1st box has 15 more balls than the 2nd box.)

--------------------------------   Add the equations


    1.4x     = 69 + 15 = 84

       x               = 84/1.4 = 60.


Thus, first box has 60 balls.

The second box has  60 - 15 = 45 balls  (and they all are red, according to the condition).

The first box has  0.4*60 = 24 red balls.

The total number of red balls is  24 + 45 = 69.   <<<---===  It is THE CHECK (!) and it is CORRECT (!)


ANSWER.  There are 60 + 45 = 105 balls, in all.

Solved.

---------------

This problem has an underwater stone.

One condition is EXCESSIVE, but FORTUNATELY, as I checked it, this excessive condition is CONSISTENT
with other two basic conditions,

making the problem CORRECTLY POSED.

When the problem has an excessive condition, the check becomes not only desired: it becomes NECESSARY.

FORTUNATELY (again), as I checked it, this excessive condition is CONSISTENT with other two basic conditions,

making the problem CORRECTLY POSED.

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