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0.0027x10^x/0.09x10^y=3x10^8 What is the value of y less than x?

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0.0027x10^x/0.09x10^y=3x10^8 What is the value of y less than x? [#permalink]

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New post Updated on: 24 Sep 2017, 14:13
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\(\frac{0.0027x10^x}{0.09x10^y}\)=3 x 10^8 What is the value of y less than x?

A 9
B 10
C 11
D 12
E 13

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Originally posted by SajjadAhmad on 24 Sep 2017, 12:18.
Last edited by SajjadAhmad on 24 Sep 2017, 14:13, edited 1 time in total.
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Re: 0.0027x10^x/0.09x10^y=3x10^8 What is the value of y less than x? [#permalink]

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New post 24 Sep 2017, 13:54
2
SajjadAhmad wrote:
\(\frac{0.0027x10^x}{0.09x10^y}\)=3x10^8 What is the value of y less than x?

A 9
B 10
C 11
D 12
E 13

In stages

\(\frac{0.0027*10^x}{0.09*10^y}\)=\(3*10^8\) REWRITE

\(\frac{27*10^{-4}*10{^x}}{9*10^{-2}*10{^y}}\) =\(3*10^8\)

Switch the negative powers of 10:

\(\frac{27*10^{2}*10^{x}}{9*10^{4}*10^{y}}\) =\(3*10^8\)

DIVIDE:

\(3*10^{(2-4)}*10^{(x-y)} = 3*10^8\)

Factor out 3

\(10^{(2-4)}*10^{(x-y)} = 10^8\)

Divide by \(10^{-2}\)

\(\frac{10^{-2}*10^{(x-y)}}{10^{-2}} = \frac{10^8}{10^{-2}}\)

Simplify:

\(10^{(x-y)} = 10^{(8- (-2))}\)

\(10^{(x-y)} = 10^{10}\)

"y less than x" means "\(x - y\)"

Bases are identical, set the exponents equal. The value of y less than x is

\(x - y = 10\)

ANSWER B

In fewer steps

\(\frac{0.0027*10^x}{0.09*10^y}\)=\(3*10^8\)

\((.03)*10^{x-y} = 3 * 10^8\)

\(3*10^{-2}*10^{x-y} = 3 * 10^8\)

\(10^{x-y} = 10^{10}\)

\(x - y = 10\)

ANSWER B


SajjadAhmad , thank you for the question. I had a hard time differentiating between what I thought was variable \(x\), and "x" as multiplication. I think it might be better to use an asterisk, as I did. JMO. :-)
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0.0027x10^x/0.09x10^y=3x10^8 What is the value of y less than x? [#permalink]

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New post 24 Sep 2017, 14:17
[/quote]"thank you for the question. I had a hard time differentiating between what I thought was variable \(x\), and "x" as multiplication. I think it might be better to use an asterisk, as I did. JMO. :-)[/quote]

Done... Thanks
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Re: 0.0027x10^x/0.09x10^y=3x10^8 What is the value of y less than x? [#permalink]

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New post 24 Sep 2017, 14:21
SajjadAhmad wrote:
\(\frac{0.0027x10^x}{0.09x10^y}\)=3 x 10^8 What is the value of y less than x?

A 9
B 10
C 11
D 12
E 13


The answer should be B as follows.

\(\frac{0.0027*10^x}{0.09*10^y}\)=3 * 10^8 ==> \(\frac{27*10^(x-4)}{9*10^(y-2)}\)=3 * 10^8 ==> \([fraction]3*10^(x-4-y+2)\)=3 * 10^8

Comparing the power of 10 on both the sides, we get

x-4-y+2=8 ==>x-y-2=8 ==>x-y=10

Hence answer B
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Re: 0.0027x10^x/0.09x10^y=3x10^8 What is the value of y less than x?   [#permalink] 24 Sep 2017, 14:21
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