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JAMB 2012 Mathematics · Question 16

Make 'n' the subject of the formula if w = v(2+cn)1−cn\frac{v(2 + cn)}{1 - cn}

Options

  1. A.1c(w−2vv+w)\frac{1}{c}(\frac{w - 2v}{v + w})
  2. B.1c(w−2vv−w)\frac{1}{c}(\frac{w - 2v}{v - w})
  3. C.1c(w+2vv−w)\frac{1}{c}(\frac{w + 2v}{v - w})
  4. D.1c(w+2vv+w)\frac{1}{c}(\frac{w + 2v}{v + w})

Answer: A. 1c(w−2vv+w)\frac{1}{c}(\frac{w - 2v}{v + w})

Explanation written with AI and checked against the answer key

Step 1: Analyze the question We need to rearrange w = v(2 + cn)/(1 − cn) so that n stands alone on one side. Step 2: Concept Clear the fraction by cross-multiplying, collect all the n-terms on one side, factor out n, then divide. Step 3: Solution w = v(2 + cn)/(1 − cn) Multiply both sides by (1 − cn): w(1 − cn) = v(2 + cn) Expand both sides: w − wcn = 2v + vcn Collect the n-terms on one side and the other terms on the other side: w − 2v = vcn + wcn Factor out cn: w − 2v = cn(v + w) Divide by c(v + w): n = (w − 2v) / [c(v + w)] That is: n = (1/c) · (w − 2v)/(v + w) Step 4: Check against the options This matches option A. Option B has (v − w) in the denominator, which would come from a sign error when moving the wcn term. Options C and D have (w + 2v) in the numerator, which would come from a sign error on the 2v term. Quick check with numbers: Let v = 1, c = 1, n = 1. Then w = 1(2 + 1)/(1 − 1), which is undefined, so pick n = 2 instead. Then w = (2 + 2)/(1 − 2) = −4. Using the formula, n = (−4 − 2)/(1 + (−4)) = (−6)/(−3) = 2 ✓. Tip: In "make the subject" questions, always expand first, then group the terms containing the subject on one side. Factorise the subject out before dividing. Watch signs carefully when moving terms across the equals sign.

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