SOLUTION: Divide 90 into two parts so that the ratio between their difference and sum is 1:9

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Question 987553: Divide 90 into two parts so that the ratio between their difference and sum is 1:9
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
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Answer.  40 and 50.

Solution

Let  x  be the smaller of the two parts.

Then the other part is  90-x.

Notice that the sum of these parts is precisely  90,  while the difference is  (90-x) - x = 90-2x.

Then,  according to the condition,

%2890-2x%29%2F90 = 1%2F9,       ----->

90+-+2x = 90%2F9,

90 - 2x = 10,

2x = 90 - 10 = 80,

x = 80%2F2 = 40.

Thus the smallest part is  40,  and the other part is  90-40 = 50.