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If [m][fraction]x/100[/fraction]+[fraction]x/1,000[/fraction
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07 Jan 2021, 06:23
07 Jan 2021, 06:23
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If \(\frac{x}{100}+\frac{x}{1,000}+\frac{x}{10,000}+\frac{x}{100,000}=111\), what is the approximation of x?
A. 11,100
B. 111,000
C. 1,111,000
D. 11,111,000
E. 111,111,000
Kudos for the right answer and explanation
A. 11,100
B. 111,000
C. 1,111,000
D. 11,111,000
E. 111,111,000
Kudos for the right answer and explanation
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If [m][fraction]x/100[/fraction]+[fraction]x/1,000[/fraction
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07 Jan 2021, 06:36
07 Jan 2021, 06:36
1
Carcass wrote:
If \(\frac{x}{100}+\frac{x}{1,000}+\frac{x}{10,000}+\frac{x}{100,000}=111\), what is the approximation of x?
A. 11,100
B. 111,000
C. 1,111,000
D. 11,111,000
E. 111,111,000
Kudos for the right answer and explanation
A. 11,100
B. 111,000
C. 1,111,000
D. 11,111,000
E. 111,111,000
Kudos for the right answer and explanation
One approach is to test the answer choices
A) 11,100
We get: 11,100/100 + 11,100/1000 + 11,100/10000 + 11,100/100000 = 111 + 11.1 +....STOP
Our sum is ALREADY greater than 111, and since the subsequent values in the sum are all positive, the sum will just get bigger and bigger
So, 11,100 is already a little too big
Since the other 4 answer choices are even bigger than 11,100, we can see that A is the best answer
Answer: A
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If [m][fraction]x/100[/fraction]+[fraction]x/1,000[/fraction
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07 Jan 2021, 06:41
07 Jan 2021, 06:41
2
Carcass wrote:
If \(\frac{x}{100}+\frac{x}{1,000}+\frac{x}{10,000}+\frac{x}{100,000}=111\), what is the approximation of x?
A. 11,100
B. 111,000
C. 1,111,000
D. 11,111,000
E. 111,111,000
Kudos for the right answer and explanation
A. 11,100
B. 111,000
C. 1,111,000
D. 11,111,000
E. 111,111,000
Kudos for the right answer and explanation
Another approach....
Take: \(\frac{x}{100}+\frac{x}{1,000}+\frac{x}{10,000}+\frac{x}{100,000}=111\)
Multiply both sides of the equation by \(100,000\) to get: \(1000x + 100x + 10x + 1x = 11,100,000\)
Simplify: \(1,111x = 11,100,000\)
So, \(x = \frac{11,100,000}{1,111} ≈ \frac{11,100,000}{1,110} ≈ 10,000\)
The answer choice that's closest to \(10,000\) is A.
