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QOTD#25 Evangeline must spend of her weekly salary on rent a
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30 Apr 2017, 14:14
30 Apr 2017, 14:14
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Question Stats:
53% (02:29) correct
46% (03:00) wrong based on 83 sessions
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Evangeline must spend \(\frac{3}{8}\) of her weekly salary on rent and \(\frac{1}{6}\) of her remaining salary on food. Which of the following could be percentages of her weekly salary that Evangeline devotes to entertainment, while still enabling her to place \(\frac{4}{9}\) of her salary into a savings account?
Indicate all such percentages.
A. 0.5%
B. 5.0%
C. 7.5%
D. 10.0%
E. 15.0%
F. 25.0%
G. 50.0%
Indicate all such percentages.
A. 0.5%
B. 5.0%
C. 7.5%
D. 10.0%
E. 15.0%
F. 25.0%
G. 50.0%
Drill 4
Question: 13
Page: 323
Question: 13
Page: 323
Re: QOTD#25 Evangeline must spend of her weekly salary on rent a
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04 May 2017, 01:35
04 May 2017, 01:35
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Explanation
The problem has percents in the answers and no real values in the question, so it’s a Hidden Plug In; the hidden variable in this case is Evangeline’s weekly salary.
To find an easy number, try multiplying the denominators in the problem: \(8 \times 6 \times 9 = 432\), so Evangeline makes \($432\)per week. Now work the problems in bite-sized pieces.
She spends \(\frac{3}{8} \times $432 = $ 162\) on rent, leaving her with \($432 - $162 = $270\).
Of that, she spends , \(\frac{1}{6}\) or $45, on food, leaving her with \($270 - $45 = $225\).
If she wants to put \(\frac{4}{9}\) of her weekly salary, or $192, into a savings account, then she can only spend \($225 - $192 = $33\) on entertainment.
Finally, use your onscreen calculator to determine that 33 is just over 7.6% of 432, so choices (A), (B), and (C) will all work.
The problem has percents in the answers and no real values in the question, so it’s a Hidden Plug In; the hidden variable in this case is Evangeline’s weekly salary.
To find an easy number, try multiplying the denominators in the problem: \(8 \times 6 \times 9 = 432\), so Evangeline makes \($432\)per week. Now work the problems in bite-sized pieces.
She spends \(\frac{3}{8} \times $432 = $ 162\) on rent, leaving her with \($432 - $162 = $270\).
Of that, she spends , \(\frac{1}{6}\) or $45, on food, leaving her with \($270 - $45 = $225\).
If she wants to put \(\frac{4}{9}\) of her weekly salary, or $192, into a savings account, then she can only spend \($225 - $192 = $33\) on entertainment.
Finally, use your onscreen calculator to determine that 33 is just over 7.6% of 432, so choices (A), (B), and (C) will all work.
General Discussion
Re: QOTD#25 Evangeline must spend of her weekly salary on rent a
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14 Dec 2018, 15:20
14 Dec 2018, 15:20
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Full disclosure: Sandy's way may be faster for you.
Let S = Weekly salary
Here is what we know
3/8(S) = rent
1/6 (5/8)S = food (because she spends 1/6 of what is remaining after rent, what is remaining after rent is 5/8 S)
4/9S = savings
And finally, the amount ratio/percentage of entertainment is unknown, we label it x.
x(s) = entertainment
Now note, if we add up all of these, we should get her total salary, no more (but possibly less)
3/8 S + 5/38 S + 4/9 S + x S <= S
3/8 + 5/38 + 4/9 S + x <= 1
x <= .076
Thus, A, B, and C are the answers.
Let S = Weekly salary
Here is what we know
3/8(S) = rent
1/6 (5/8)S = food (because she spends 1/6 of what is remaining after rent, what is remaining after rent is 5/8 S)
4/9S = savings
And finally, the amount ratio/percentage of entertainment is unknown, we label it x.
x(s) = entertainment
Now note, if we add up all of these, we should get her total salary, no more (but possibly less)
3/8 S + 5/38 S + 4/9 S + x S <= S
3/8 + 5/38 + 4/9 S + x <= 1
x <= .076
Thus, A, B, and C are the answers.
