Discussion
When x is added to each of the numbers 4, 10, 12 and 24, then the numbers so obtained in this order are in proportion. What is the value of (3x + 1)?
Answer: B
The value of \((3x + 1)\) is 13.
Four numbers are in proportion when the product of the extremes equals the product of the means.
\[ \begin{aligned} (4 + x)(24 + x) &= (10 + x)(12 + x) \\ 96 + 28x + x^{2} &= 120 + 22x + x^{2} \\ 6x &= 24 \\ x &= 4 \end{aligned} \]
Check: the numbers become 8, 14, 16, 28, and \(8 : 14 = 16 : 28 = 4 : 7\). So \(3x + 1 = 13\). The value 16 is \(4x\), and 10 and 19 would need \(x = 3\) and \(x = 6\), which do not make the numbers proportional.
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