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Question
What number must be added to each of the numbers 4, 6, 8, 11 in order to get the four numbers in proportion?
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Solution
Let x be added to make them in proportion.
∴ (4 + x) : (6 + x) :: (8 + x) : (11 + x)
⇒ `(4 + x)/(6 + x) = (8 + x)/(11 + x)`
⇒ (4 + x) (11 + x) = (6 + x) (8 + x)
Left side:
4 × 11 + 4x + 11x + x2 = 44 + 15x + x2
Right side:
6 × 8 + 6x + 8x + x2 = 48 + 14x + x2
⇒ 44 + 15x + x2 = 48 + 14x + x2
⇒ 44 + 15x = 48 + 14x
⇒ 15x − 14x = 48 − 44
⇒ x = 4
∴ The number to be added is 4.
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