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If N = K/(T + x/y), where T = K/5 and x = 5 – T which of the following

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If N = K/(T + x/y), where T = K/5 and x = 5 – T which of the following  [#permalink]

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New post 21 Sep 2019, 05:11
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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. \(\frac{N(5 - T)}{5}\)


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Re: If N = K/(T + x/y), where T = K/5 and x = 5 – T which of the following  [#permalink]

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New post 21 Sep 2019, 05:18
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Substituting K and x from given

N = 5T / (T+(5-T)/Y)

T + (5-T) / Y = 5T / N

(5 - T ) / Y = (5T - NT)/N

Y = (5-T) N / T(5-N)
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Re: If N = K/(T + x/y), where T = K/5 and x = 5 – T which of the following  [#permalink]

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New post 21 Sep 2019, 06:01
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N=5TY/TY+5-T
NTY+5N-NT=5TY
Y(NT-5T)=NT-N5
Y=N(T-5)/T(N-5) = \(\frac{N(5 - T)}{T(5 - N)}\)
IMO A


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. \(\frac{N(5 - T)}{5}\)


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If N = K/(T + x/y), where T = K/5 and x = 5 – T which of the following  [#permalink]

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New post 01 Nov 2019, 17:37
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Every Step Described:

Step 1: substitute k and x out.

K=5T
X=5-T

In the first equation, plug in the values above in place of x and y

N = 5T/T +\(\frac{(5-T)}{Y}\)

Step 2: Multiply both sides by T+\(\frac{(5-t)}{y}\) .

Now we have N(T+\(\frac{(5-t)}{y}\)) = 5T

Step 3: Multiply both sides by y in order to cancel our fractions.

Now we have NTY + 5(N-T) = 5TY

Step 4: Subtract both sides by NTY in order to get Y on a side by itself.

Now we have 5(N-T) = 5TY - NTY

Step 5: Break out the TY on the RHS and the N on the LHS

TY(5-N) = N(5-T)

Step 6: Divide both sides by T(5-N) in order to get Y on the LHS by itself.

Now we have Y = \(\frac{N(5-T)}{T(5-N)}\)

A
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Re: If N = K/(T + x/y), where T = K/5 and x = 5 – T which of the following  [#permalink]

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New post 05 Nov 2019, 18:28
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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


K = 5T
x = 5 - T

N = 5T/(T + (5-T)/y) => N = 5ty/(Ty + 5 - T) => NTy + 5N - NT = 5Ty => y = N(5-T)/(T(5-N))

ANSWER = A
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Re: If N = K/(T + x/y), where T = K/5 and x = 5 – T which of the following  [#permalink]

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New post 12 Nov 2019, 00:27
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MikeScarn wrote:
Every Step Described:

Step 1: substitute k and x out.

K=5T
X=5-T

In the first equation, plug in the values above in place of x and y

N = 5T/T +\(\frac{(5-T)}{Y}\)

Step 2: Multiply top and bottom of the RHS (right hand side) by \(\frac{y}{y}\)

5T/T +\(\frac{(5-T)}{Y}\) multiplied by \(\frac{y}{y}\) = \(\frac{5TY}{(TY+5-T)}\)


So now we have N = \(\frac{5TY}{(TY+5-T)}\)

Step 3: Multiply both sides by the RHS denominator.

N * (TY+5-T) = \(\frac{5TY}{(TY+5-T)}\) * (TY+5-T)

The denominator cancels out

N(TY+5-T) = 5TY

Multiply the N

NTY + 5N - NT = 5TY

Step 4: Get "like terms" on the same side by adding and subtracting. Get terms with Y on the LHS.

NTY - 5TY = NT - 5N

Step 5: Separate out the Y on the LHS and the N on the RHS

Y(NT-5T) = N(T-5)

Step 6: Get Y on the LHS by itself. Do this by dividing both sides by (NT-5T)

Y = \(\frac{N(T-5)}{(NT-5T)}\)

Y = \(\frac{N(T-5)}{T(N-5)}\)


Isn't this the wrong answer
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If N = K/(T + x/y), where T = K/5 and x = 5 – T which of the following  [#permalink]

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New post 16 Nov 2019, 07:09
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N=K/(T+x/y)

N=Ky/ (Ty+x)

NTy + Nx = Ky

Nx = (NT-K)*y

(Nx)/ (NT-K) = y

Substitute K=5T and x= 5-T

A it is.


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If N = K/(T + x/y), where T = K/5 and x = 5 – T which of the following  [#permalink]

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New post 06 Dec 2019, 11:09
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chrtpmdr wrote:
@Mikescarn Isn't this the wrong answer

Yes, I have corrected my explanation.

Thanks!
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Re: If N = K/(T + x/y), where T = K/5 and x = 5 – T which of the following  [#permalink]

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New post 13 Dec 2019, 12:35
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Hi All,

We're given 3 equations to work with (which I'm going to write in increasing order of complexity):
X = 5 - T
T = K/5
N = K/(T + (X/Y))

We're asked for the value of Y in terms of N and T. Most questions that use the phrase "in terms of" are meant to be solved with Algebra. This one can also be solved by TESTing VALUES - and there's a great shortcut in how the answers are written, so if you choose easy numbers to work with, then you can save a lot of time when working through the answers).

IF..... T = 4, then X = 1 and K = 20

When we place those values into the 3rd equation (above), we end up with....
N = 20/(4 + (1/Y))

We want to make the value of Y as simple as possible (since that's what we're solving for), so let's TEST Y = 1... which means that N = 4. At this point we have the values of 5 variables....

T = 4
X = 1
K = 20
Y = 1
N = 4

This certainly looks like a lot of data to keep track of, but it's actually really straight-forward. The answers ask us to deal with just 2 of the variables (N and T). Here, BOTH of those values are equal to 4. We're asked to find the value of Y, which we chose as 1. In simple terms, any time you see a variable in an answer, you should plug-in a "4"... and we're looking for a result that equals 1. There's only one answer that matches....

Final Answer:

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Re: If N = K/(T + x/y), where T = K/5 and x = 5 – T which of the following  [#permalink]

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New post 19 Dec 2019, 19:44
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. \(\frac{N(5 - T)}{5}\)


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k=5T; x=5-T
N*(T+(x/y)) = k
N*(Ty+x) = ky
NTy+Nx = 5Ty
NTy-5Ty = -Nx
y(NT-5T) = -N(5-T)
y(NT-5T) = NT - 5N
y = (NT-5N)/(NT-5T)
y = N(T-5)/T(N-5)
y = -N(5-T)/-T(5-N)
y = N(5-T)/T(5-N)


[option a]
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Re: If N = K/(T + x/y), where T = K/5 and x = 5 – T which of the following   [#permalink] 19 Dec 2019, 19:44
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