Given:
The sum of the two quantities equals six times their difference:
x + y = 6(x - y)
Solution:
Expand and simplify the equation:
x + y = 6x - 6y
Rearranging terms:
x - 6x + y + 6y = 0
-5x + 7y = 0
Solve for the ratio:
Rewriting the equation:
5x = 7y
x / y = 7 / 5
The ratio of the two quantities is 7:5.
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