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31 Jul 2025, 09:51
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On Monday, Elena had a certain amount of money in her savings account. On Tuesday, she increased that amount by \(m\) percent. On Wednesday, she withdrew \(n\) percent of her Tuesday's closing balance, leaving her with exactly 50 percent of what she had on Monday. What is the value of \(n\) in terms of \(m\)?
A. \(\frac{100(m + 50)}{m + 100}\)
B. \(\frac{100(m - 50)}{m + 100}\)
C. \(\frac{100(m + 50)}{100 - m}\)
D. \( \frac{100m}{m + 100}\)
E. \(\frac{100(50 - m)}{m - 100}\)
A. \(\frac{100(m + 50)}{m + 100}\)
B. \(\frac{100(m - 50)}{m + 100}\)
C. \(\frac{100(m + 50)}{100 - m}\)
D. \( \frac{100m}{m + 100}\)
E. \(\frac{100(50 - m)}{m - 100}\)
31 Jul 2025, 09:51
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Official Solution:
On Monday, Elena had a certain amount of money in her savings account. On Tuesday, she increased that amount by \(m\) percent. On Wednesday, she withdrew \(n\) percent of her Tuesday's closing balance, leaving her with exactly 50 percent of what she had on Monday. What is the value of \(n\) in terms of \(m\)?
A. \(\frac{100(m + 50)}{m + 100}\)
B. \(\frac{100(m - 50)}{m + 100}\)
C. \(\frac{100(m + 50)}{100 - m}\)
D. \( \frac{100m}{m + 100}\)
E. \(\frac{100(50 - m)}{m - 100}\)
Assuming she had \($x\) on Monday, then:
On Tuesday, she’d have \(x(1 + \frac{m}{100})\)
On Wednesday, she’d have \(x(1 + \frac{m}{100}) (1 - \frac{n}{100})\)
Since that amount was 50 percent of what she had on Monday, then:
\(x(1 + \frac{m}{100}) (1 - \frac{n}{100}) =\frac{x}{2}\)
\((1 + \frac{m}{100}) (1 - \frac{n}{100}) =\frac{1}{2}\)
\((\frac{100 + m}{100}) (1 - \frac{n}{100}) =\frac{1}{2}\)
\((1 - \frac{n}{100}) =\frac{50}{100 + m }\)
\(\frac{100 - n}{100} =\frac{50}{100 + m }\)
\(100 - n =\frac{5,000}{100 + m }\)
\(n = 100 - \frac{5,000}{100 + m }\)
\(n = \frac{10,000 + 100m - 5,000}{100 + m }\)
\(n = \frac{5,000 + 100m}{100 + m }\)
\(n = \frac{100(50 + m)}{100 + m }\)
Answer: A
On Monday, Elena had a certain amount of money in her savings account. On Tuesday, she increased that amount by \(m\) percent. On Wednesday, she withdrew \(n\) percent of her Tuesday's closing balance, leaving her with exactly 50 percent of what she had on Monday. What is the value of \(n\) in terms of \(m\)?
A. \(\frac{100(m + 50)}{m + 100}\)
B. \(\frac{100(m - 50)}{m + 100}\)
C. \(\frac{100(m + 50)}{100 - m}\)
D. \( \frac{100m}{m + 100}\)
E. \(\frac{100(50 - m)}{m - 100}\)
Assuming she had \($x\) on Monday, then:
On Tuesday, she’d have \(x(1 + \frac{m}{100})\)
On Wednesday, she’d have \(x(1 + \frac{m}{100}) (1 - \frac{n}{100})\)
Since that amount was 50 percent of what she had on Monday, then:
\(x(1 + \frac{m}{100}) (1 - \frac{n}{100}) =\frac{x}{2}\)
\((1 + \frac{m}{100}) (1 - \frac{n}{100}) =\frac{1}{2}\)
\((\frac{100 + m}{100}) (1 - \frac{n}{100}) =\frac{1}{2}\)
\((1 - \frac{n}{100}) =\frac{50}{100 + m }\)
\(\frac{100 - n}{100} =\frac{50}{100 + m }\)
\(100 - n =\frac{5,000}{100 + m }\)
\(n = 100 - \frac{5,000}{100 + m }\)
\(n = \frac{10,000 + 100m - 5,000}{100 + m }\)
\(n = \frac{5,000 + 100m}{100 + m }\)
\(n = \frac{100(50 + m)}{100 + m }\)
Answer: A
