Two numbers are in the ratio 7:5. When each number is decreased by 4 the ratio is 5:7. Find the sum of two numbers
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Let the numbers be 5x and 7x.
(5x-9):(7x-9) = 7:11, or
49x-63 = 55x-99. or
6x = 36, or x = 6.
So the numbers are 30 and 42. The difference between them is 2x or 12.
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