What number must be subtracted from each of the numbers $27, 38, 7, 8$ , so that the remainders are in proportion?

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Solution

$27, 38, 7, 8$
Let $x$ be subtracted $(27 - x), (38 - x), (7 - x), (8 - x)$
So
$(27 - x) (7 - x) = (38 - x) (8 - x)$
$189 - 27 x - 7 x + x^{2} = 304 - 38 x - 8 x + x^{2}$
$189 - 34 x = 304 - 46 x$
$46 x - 34 x = 304 - 189$
$12 x = 115$
$x = \frac{115}{12}$
$x = 9.58$

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