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Question
If the same number be added to the numbers 5, 11, 15 and 31, the resulting numbers are in proportion. Find the number.
Solution
Let x be added to each number, then the numbers will be 5 + x, 11 + x, 15 + x and 31 + x
According to the condition
`(5 + x)/(11 + x) = (15 + x)/(31 + x)`
By cross multiplication,
(5 + x)(31 + x) = (15 + x)(11 + x)
⇒ 155 + 5x + 31x + x2 = 165 + 11x + 15x + x2
⇒ 155 + 36x + x2 = 165 + 26x + x2
⇒ 36x + x2 - 26x - x2 = 165 - 155
⇒ 10x = 10 ⇒ x = `10/10 = 1`
1 should be added
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