gmatt1476 wrote:
If \(N = \frac{K}{T + \frac{x}{y}}\), where \(T = \frac{K}{5}\) and \(x = 5 – T\), which of the following expresses y in terms of N and T ?
A. \(\frac{N(5 - T)}{T(5 - N)}\)
B. \(\frac{N(T - 5)}{T(5 - N)}\)
C. \(\frac{5 - T}{T(5 - N)}\)
D. \(\frac{5N(5 - T)}{T(1 - 5N)}\)
E. \(\frac{N(5 - T)}{5}\)
PS47302.01
\(N = \frac{K}{T + \frac{x}{y}}\)
We are asked to express \(y\) in terms of \(N\) and \(T\). In other words we need to replace \(K\) and \(x\) with expressions in terms of \(N\) and/or \(T\)
1. Replacing \(K\) with \(5T\) and \(x\) with \(5 - T\) in the equation
2. \(N = \frac{5T}{T + \frac{5 - T}{y}} = \frac{5Ty}{Ty + 5 - T}\)
3. \(NTy + 5N - TN = 5Ty\)
4. \(NTy - 5Ty = TN - 5N\)
5. \(Ty(N - 5) = N(T - 5)\)
6. \(y = \frac{N(T - 5)}{T(N - 5)}\); this does not match any of the answer options, but if you observe closely then if you multiply the numerator and denominator with -1 then the equation matches option A
7. \(y = \frac{(-1) * N(T - 5)}{(-1) * T(N - 5)} = \frac{N(5 - T)}{T(5 - N)}\)
Ans.
A _________________
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