Discussion
If we have to make numbers 8, 12, 16 and 22 in proportion, what number must be added to each number?
Answer: B
Four numbers a, b, c and d are in proportion when \(a : b = c : d\), that is, \(a \times d = b \times c\). Let x be added to each of 8, 12, 16 and 22.
\[ (8 + x)(22 + x) = (12 + x)(16 + x) \]
\[ 176 + 30x + x^2 = 192 + 28x + x^2 \] \[ 2x = 16 \Rightarrow x = 8 \]
Check: 16, 20, 24 and 30 have 16 : 20 = 24 : 30 = 4 : 5. The values 7, 9 and 10 do not make the products equal. The answer is 8, option B.
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