SOLUTION: Two positive numbers are in a ratio of 9 to 10. If the lesser number is decreased by 6 and the greater number is decreased by 25, the resulting ratio is 2 to 1. Find the greatest o

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Two positive numbers are in a ratio of 9 to 10. If the lesser number is decreased by 6 and the greater number is decreased by 25, the resulting ratio is 2 to 1. Find the greatest o      Log On


   

Question 22763: Two positive numbers are in a ratio of 9 to 10. If the lesser number is decreased by 6 and the greater number is decreased by 25, the resulting ratio is 2 to 1. Find the greatest of the original numbers.
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
Let larger number be x

We have the 2 numbers in ratio 9:10, so smaller number must be 9x/10

Now change numbers:

lefthand number reduces to (9x/10) - 6
righthand number reduces to x - 25

And now the LH number is twice the size of RH number, ie:

(9x/10) - 6 = 2(x-25) So solve this...
(9x/10) - 6 = 2x-50
(9x/10) = 2x-44
9x = 20x-440
11x = 440
--> x = 40
9/10ths of this is 36

so the 2 numbers are 36 and 40.

do the check too:

36-6 is 30
40-25 is 15, half of 30.

jon.