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What number must be added to each of the numbers 5, 9, 17, 27 to make new numbers in proportion? |
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Answer» Let the number to be added be x. Then the numbers 5, 9, 17, 27 will be 5 + x, 9 + x, 17 + x, 27 + x. Given that new numbers are in proportional, i.e., 5 + x : 9 + x :: 17 + x : 27 + x. ⇒ \(\frac{5+x}{9+x}\) = \(\frac{17+x}{27+x}\) ⇒ (5 + x)(27 + x) = (9 + x)(17 + x) ⇒ x2 + 32x + 135 = x2 + 26x + 153 ⇒ 32x − 26x = 153 − 135 ⇒ 6 = 18 ⇒ x = \(\frac{18}{6}\) = 3. |
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