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

Question 987553: Divide 90 into two parts so that the ratio between their difference and sum is 1:9

Answer by ikleyn(52786) (Show Source): You can put this solution on YOUR website!
.
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,

= , ----->

= ,

90 - 2x = 10,

2x = 90 - 10 = 80,

x = = 40.

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

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