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Sum

If the same number be added to the numbers 5, 11, 15 and 31, the resulting numbers are in proportion. Find the number.

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#### 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 + x^{2} = 165 + 11x + 15x + x^{2}

⇒ 155 + 36x + x^{2} = 165 + 26x + x^{2}

⇒ 36x + x^{2} - 26x - x^{2} = 165 - 155

⇒ 10x = 10 ⇒ x = `10/10 = 1`

1 should be added

Concept: Solving Linear Inequations

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