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MrWhite
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From her gross pay of g dollars, Larissa deducted t percent to pay tax 08 Dec 2023, 21:43
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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55% (hard)

Question Stats:

74% (02:51) correct 26% (03:21) wrong based on 459 sessions

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From her gross pay of g dollars, Larissa deducted t percent to pay taxes. Then she deposited into a savings account s dollars of the amount that remained after her tax payment. Finally, she donated to charity c percent of the amount that remained after her savings deposit. In terms of g, t, s, and c, what amount in dollars, of Larissa's gross pay remained after her donation to charity?

(A) \(\frac{((100 - t)g - 100s)(100 - c) }{ 10^4}\)

(B) \(\frac{gt - (100 - t)s - (100 - c) }{ 10^4}\)

(C) \(\frac{(g - s)(100 - t)(100 - c) }{ 10^4}\)

(D) \(\frac{(100 - t)g - 100s - 100c }{ 10^4}\)

(E) \(\frac{100(g - s) - t - c }{ 10^4}\)
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From her gross pay of g dollars, Larissa deducted t percent to pay tax 09 Dec 2023, 00:24
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MrWhite
From her gross pay of g dollars, Larissa deducted t percent to pay taxes. Then she deposited into a savings account s dollars of the amount that remained after her tax payment. Finally, she donated to charity c percent of the amount that remained after her savings deposit. In terms of g, t, s, and c, what amount in dollars, of Larissa's gross pay remained after her donation to charity?

(A) \(\frac{((100 - t)g - 100s)(100 - c) }{ 10^4}\)

(B) \(\frac{gt - (100 - t)s - (100 - c) }{ 10^4}\)

(C) \(\frac{(g - s)(100 - t)(100 - c) }{ 10^4}\)

(D) \(\frac{(100 - t)g - 100s - 100c }{ 10^4}\)

(E) \(\frac{100(g - s) - t - c }{ 10^4}\)

Gross pay = g dollars;

The remainder after paying t% of taxes =

    \(g(1 - \frac{t}{100}) = g(\frac{100 - t}{100})=\frac{g(100 - t)}{100}\).

The remainder after depositing s dollars =

    \(\frac{g(100 - t)}{100}- s=\frac{g(100 - t)-100s}{100}\).

The remainder after donating c% to charity =

    \(\frac{g(100 - t)-100s}{100}*(1 - \frac{c}{100})=\frac{g(100 - t)-100s}{100}*\frac{100-c}{100}=\frac{(g(100 - t)-100s)(100-c)}{10^4}\).

Answer: A.
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From her gross pay of g dollars, Larissa deducted t percent to pay tax 08 Dec 2023, 22:44
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MrWhite
From her gross pay of g dollars, Larissa deducted t percent to pay taxes. Then she deposited into a savings account s dollars of the amount that remained after her tax payment. Finally, she donated to charity c percent of the amount that remained after her savings deposit. In terms of g, t, s, and c, what amount in dollars, of Larissa's gross pay remained after her donation to charity?

(A) \(\frac{((100 - t)g - 100s)(100 - c) }{ 10^4}\)
(B) \(\frac{gt - (100 - t)s - (100 - c) }{ 10^4}\)
(C) \(\frac{(g - s)(100 - t)(100 - c) }{ 10^4}\)
(D) \(\frac{(100 - t)g - 100s - 100c }{ 10^4}\)
(E) \(\frac{100(g - s) - t - c }{ 10^4}\)

OA is A

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From her gross pay of g dollars, Larissa deducted t percent to pay tax 09 Dec 2023, 21:33
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MrWhite
From her gross pay of g dollars, Larissa deducted t percent to pay taxes. Then she deposited into a savings account s dollars of the amount that remained after her tax payment. Finally, she donated to charity c percent of the amount that remained after her savings deposit. In terms of g, t, s, and c, what amount in dollars, of Larissa's gross pay remained after her donation to charity?

(A) \(\frac{((100 - t)g - 100s)(100 - c) }{ 10^4}\)

(B) \(\frac{gt - (100 - t)s - (100 - c) }{ 10^4}\)

(C) \(\frac{(g - s)(100 - t)(100 - c) }{ 10^4}\)

(D) \(\frac{(100 - t)g - 100s - 100c }{ 10^4}\)

(E) \(\frac{100(g - s) - t - c }{ 10^4}\)


To find the amount in dollars of Larissa's gross pay that remained after her donation to charity, we need to follow the sequence of deductions and deposits she made, in terms of g, t, s, and c

Tax Deduction:
Larissa deducted t% of her gross pay g for taxes. The amount deducted for taxes is g×t/100. The amount remaining after tax deduction is g − g×t/100

Savings Deposit:
After paying taxes, Larissa deposited s dollars into a savings account.
The amount remaining after the savings deposit is g − g×t/100 − s

Charity Donation:
She then donated c% of the remaining amount after her savings deposit to charity. The amount donated to charity is (g − g×t/100 − s)×c/100

The final amount remaining after her donation to charity is (g − g×t/100 − s) - [(g − g×t/100 − s)×c/100]

Simplifying, we get ((100 - t)g - 100s)(100 - c) / 10^4 which is option A
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From her gross pay of g dollars, Larissa deducted t percent to pay tax 15 Dec 2024, 11:52
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