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Alice earns d dollars and has t percent

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Alice earns d dollars and has t percent [#permalink] New post 01 Feb 2016, 03:52
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85% (00:38) correct 14% (01:50) wrong based on 14 sessions
Alice earns d dollars and has t percent of what she earns deducted for taxes. How much of what she earns does Alice have left after taxes?

A) d(1−100t) dollars
B) d(1−10t) dollars
C) d(1−t) dollars
D) d(1−0.1t) dollars
E) d(1−0.01t) dollars

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Question: 23
Page: 471
Difficulty: easy/medium
[Reveal] Spoiler: OA

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Re: Alice earns d dollars and has t percent [#permalink] New post 01 Feb 2016, 03:57
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Solution

We know that \(t\) percent can be expressed as \(\frac{t}{100}\) , or \(0.01t\).

The amount that Alice has deducted for taxes, which is t percent of d dollars, can be expressed as \(0.01td\) dollars. The amount that Alice has left after taxes is the amount that she earns minus the amount that she has deducted for taxes, or d−0.01td dollars.

Taking d common we have \(d(1 - 0.01t)\). Hence option E is the right choice.
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Re: Alice earns d dollars and has t percent [#permalink] New post 28 Feb 2018, 12:36
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sandy wrote:
Alice earns d dollars and has t percent of what she earns deducted for taxes. How much of what she earns does Alice have left after taxes?

A) d(1 − 100t) dollars
B) d(1 − 10t) dollars
C) d(1 − t) dollars
D) d(1 − 0.1t) dollars
E) d(1 − 0.01t) dollars


t percent = t/100

So, t percent of d dollars = (t/100)(d)
In other words, (t/100)(d) is DEDUCTED from Alice's pay (of d dollars)

So, the amount remaining = d - (t/100)(d) Check the answer choices.....not there! Looks like we need to rewrite our answer to match one of the answer choice.

So, take: d - (t/100)(d)
Factor out the d to get: d(1 - t/100) ....still not among the answer choices!

Notice that t/100 = (t)(1/100)
= (t)(0.01)
0.01t

So, take: d(1 - t/100) and rewrite as d(1 - 0.01t)

Answer: E

Cheers,
Brent
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Re: Alice earns d dollars and has t percent [#permalink] New post 02 Mar 2018, 05:13
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If you have a hard time with this one, just come up with some hypothetical numbers and see which answer works.

If Alice earned 100 dollars and she paid 10% in taxes, we can easily see she would bring home 90 dollars since 10% of 100 is 90. Choice E is the only one that would give us 90.

D(1 - 0,01T)
100(1 - 0.01(10))
100(0.9)
90

Answer E
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Re: Alice earns d dollars and has t percent [#permalink] New post 06 May 2018, 16:34
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sandy wrote:
Alice earns d dollars and has t percent of what she earns deducted for taxes. How much of what she earns does Alice have left after taxes?

A) d(1−100t) dollars
B) d(1−10t) dollars
C) d(1−t) dollars
D) d(1−0.1t) dollars
E) d(1−0.01t) dollars


After taxes, Alice has d(1 - t/100) = d(1 - 0.01t) dollars left.

Answer: E
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Re: Alice earns d dollars and has t percent   [#permalink] 06 May 2018, 16:34
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