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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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Joined: 02 Nov 2016
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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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Updated on: 20 Dec 2018, 10:37
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Difficulty:

15% (low)

Question Stats:

82% (01:52) correct 18% (02:15) wrong based on 83 sessions

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$$\frac{0.0027*10^x}{0.09*10^y}$$=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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Last edited by SajjadAhmad on 20 Dec 2018, 10:37, edited 3 times in total.
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Joined: 22 May 2016
Posts: 3548
Re: 0.0027x10^x/0.09x10^y=3x10^8 What is the value of y less than x?  [#permalink]

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24 Sep 2017, 13:54
3
1
$$\frac{0.0027x10^x}{0.09x10^y}$$=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

$$x - y = 10$$

In fewer steps

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

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

$$3*10^{-2}*10^{x-y} = 3 * 10^8$$

$$10^{x-y} = 10^{10}$$

$$x - y = 10$$

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

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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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24 Sep 2017, 14:21
$$\frac{0.0027x10^x}{0.09x10^y}$$=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

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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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20 Dec 2018, 09:26
$$\frac{0.0027x10^x}{0.09x10^y}$$=3 x 10^8 What is the value of y less than x?

A 9
B 10
C 11
D 12
E 13

Dear Moderator,
In this question, the multiplication, symbol, looks like the variable x , making the question very confusing. Is it possible to format the question properly? Thank you.
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- Stne
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Posts: 58402
Re: 0.0027x10^x/0.09x10^y=3x10^8 What is the value of y less than x?  [#permalink]

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20 Dec 2018, 09:29
stne 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

Dear Moderator,
In this question, the multiplication, symbol, looks like the variable x , making the question very confusing. Is it possible to format the question properly? Thank you.

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Edited. Thank you.
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Re: 0.0027x10^x/0.09x10^y=3x10^8 What is the value of y less than x?   [#permalink] 20 Dec 2018, 09:29
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