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Re: Direct and inverse proportionality [#permalink]
06 Jun 2011, 00:34

According to expression Q= 5w/4xz² now, w'=4w, x'=2x z'=3z Put these values in a same order, we get Q'= 5(4w)/4(2x)(3z)² Q'=5w/18xz² Q'=2/9*(5w/4xz²) So, Q'= 2/9(Q),q will be a multiple of factor 2/9. This is the most effective way to solve such question.

Re: Direct and inverse proportionality [#permalink]
22 Feb 2012, 23:08

Expert's post

SergeNew wrote:

Hi guys,

I am sorry, but i still did not get this part.

Q'=5w/18xz² to Q'=2/9*(5w/4xz²)

Would anyone be able please to elaborate on it? I would really appreciate it.

Serge.

If the function Q is defined by the formula Q = 5w/(4x(z^2)), by what factor will Q be multiplied if w is quadrupled, x is doubled, and z is tripled? A. 1/9 B. 2/9 C. 4/9 D. 3/9 E. 2/27

Given: Q=\frac{5w}{4x*z^2}.

Now, quadruple w, so make it 4w; double x so make it 2x; triple z and substitute these values instead of x, y, and z in the original equation:

\frac{5(4w)}{4(2x)*(3z)^2}=\frac{4*5w}{4*2x*9*z^2}=\frac{4*5w}{18*(4x*z^2)}=\frac{4}{18}*\frac{5w}{4x*z^2}=\frac{2}{9}*\frac{5w}{4x*z^2}. Thus Q is multiplied by \frac{2}{9}.

Answer: B.

Else plug-in values for x, y, and z. Let x=y=z=1 --> Q=\frac{5w}{4x*z^2}=\frac{5}{4}.

4w=4, 2x=2 and 3z=3 --> \frac{5*4}{4*2*3^2}=\frac{4}{18}*\frac{5}{4}=\frac{2}{9}*\frac{5}{4}. Thus Q is multiplied by \frac{2}{9}.