What should be added to each of the numbers 3, 5, 13 and 19 so that the resulting numbers may be in proportion?

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Solution

Dear Student,
$L e t t h e n u m b e r t o b e a d d e d b e x . t h e n u m b e r s 3, 5, 13, 19 w i l l b e 3 + x, 5 + x, 13 + x, 19 + x t h e r e f o r e : \frac{3 + x}{5 + x} = \frac{13 + x}{19 + x} (3 + x) (19 + x) = (13 + x) (5 + x) 57 + 3 x + 19 x + x^{2} = 65 + 13 x + 5 x + x^{2} 57 + 22 x = 65 + 18 x 65 - 57 = 22 x - 18 x 8 = 4 x x = 2$
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