Question

What number should be added to each one of 6,14,18,38 to make equally proportionate?

Answer 1

Let us add x to each of the four numbers to get (6+x):(14+x)::(18+x):(38+x). The product of the ends = the product of the means, or

(6+x)(38+x) = (14+x)(18+x), or

x^2 + 44x + 228 = x^2 + 32x + 252, or

44x - 32x = 252–228, or

12x = 24, or x =2.

Check: 8:16::20:40 or 8*40 = 320 same as 16*20 - 320. Correct.

Hence 2 needs to be added to each of the 4 numbers - 6, 14, 18 and 38 to make the resulting numbers in proportion.

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