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(52903)   (Show Source):
You can put this solution on YOUR website! .
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.
|
|
|
