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From her gross pay of g dollars, Larissa deducted t percent to pay tax
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08 Dec 2023, 21:43
08 Dec 2023, 21:43
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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) \(\frac{100(g - s) - t - c }{ 10^4}\)
(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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Re: From her gross pay of g dollars, Larissa deducted t percent to pay tax
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08 Dec 2023, 22:44
08 Dec 2023, 22:44
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MrWhite wrote:
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) \(\frac{100(g - s) - t - c }{ 10^4}\)
(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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Re: From her gross pay of g dollars, Larissa deducted t percent to pay tax
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09 Dec 2023, 00:24
09 Dec 2023, 00:24
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MrWhite wrote:
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) \(\frac{100(g - s) - t - c }{ 10^4}\)
(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.
