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In 1990, twice as many boys as girls at Adams High School ea
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24 Jan 2019, 06:22
24 Jan 2019, 06:22
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In 1990, twice as many boys as girls at Adams High School earned varsity letters. From 1990 to 2000 the number of girls earning varsity letters increased by 25% while the number of boys earning varsity letters decreased by 25%. What was the ratio in 2000 of the number of girls to the number of boys who earned varsity letters?
A. \(\frac{5}{3}\)
B. \(\frac{6}{5}\)
C. \(1\)
D. \(\frac{5}{6}\)
E. \(\frac{3}{5}\)
A. \(\frac{5}{3}\)
B. \(\frac{6}{5}\)
C. \(1\)
D. \(\frac{5}{6}\)
E. \(\frac{3}{5}\)
Re: In 1990, twice as many boys as girls at Adams High School ea
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25 Jan 2019, 19:40
25 Jan 2019, 19:40
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1
Let the number of girls who earned varsity letters be x
then the number of boys who earned varsity letters will be 2x
Now, the number of girls who earned varsity letters increased by \(25%\) in 1 decade.
Therefore, the number of girls at the end of 2000 is \(1.25x\)
In the same time number of boys decreased by \(25%\) therefore their population will be \(0.75*2x = 1.5x\)
Hence, the ratio is \(\frac{125}{150} = \frac{5}{6}\)
then the number of boys who earned varsity letters will be 2x
Now, the number of girls who earned varsity letters increased by \(25%\) in 1 decade.
Therefore, the number of girls at the end of 2000 is \(1.25x\)
In the same time number of boys decreased by \(25%\) therefore their population will be \(0.75*2x = 1.5x\)
Hence, the ratio is \(\frac{125}{150} = \frac{5}{6}\)
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Re: In 1990, twice as many boys as girls at Adams High School ea
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30 Dec 2024, 19:12
30 Dec 2024, 19:12
In 1990
Twice as many boys as girls at Adams High School earned varsity letters.
=> \(B_{1990} = 2 * G_{1990}\)
In 2000
From 1990 to 2000 the number of girls earning varsity letters increased by 25%
=> \(G_{2000} = G_{1990} + 0.25 * G_{1990} = 1.25 * G_{1990}\)
While the number of boys earning varsity letters decreased by 25%.
=> \(B_{2000} = B_{1990} - 0.25 * B_{1990} = 0.75 * B_{1990} = 0.75 * 2 * G_{1990} = 1.50 * G_{1990}\)
What was the ratio in 2000 of the number of girls to the number of boys who earned varsity letters?
=> \(\frac{ G_{2000}}{ B_{2000} }\) = \(\frac{ 1.25 * G_{1990} }{ 1.50 * G_{1990} }\) = \(\frac{ 125}{150}\) = \(\frac{ 5}{6}\)
So, Answer will be D
Hope it helps!
Twice as many boys as girls at Adams High School earned varsity letters.
=> \(B_{1990} = 2 * G_{1990}\)
In 2000
From 1990 to 2000 the number of girls earning varsity letters increased by 25%
=> \(G_{2000} = G_{1990} + 0.25 * G_{1990} = 1.25 * G_{1990}\)
While the number of boys earning varsity letters decreased by 25%.
=> \(B_{2000} = B_{1990} - 0.25 * B_{1990} = 0.75 * B_{1990} = 0.75 * 2 * G_{1990} = 1.50 * G_{1990}\)
What was the ratio in 2000 of the number of girls to the number of boys who earned varsity letters?
=> \(\frac{ G_{2000}}{ B_{2000} }\) = \(\frac{ 1.25 * G_{1990} }{ 1.50 * G_{1990} }\) = \(\frac{ 125}{150}\) = \(\frac{ 5}{6}\)
So, Answer will be D
Hope it helps!
