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30 Dec 2024, 06:56
Kudos
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
66% (01:00) correct
33% (00:57) wrong based on 3 sessions
History
Date
Time
Result
Not Attempted Yet
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. 5/3
B. 6/5
C. 1/1
D. 5/6
E. 3/5
A. 5/3
B. 6/5
C. 1/1
D. 5/6
E. 3/5
30 Dec 2024, 20:11
Kudos
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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!
01 Jan 2025, 10:26
Kudos
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OE
A nice way to answer this question is to pick easy-to-use numbers. Assume that in 1990 there were 200 boys and 100 girls who earned varsity letters. Then in 2000, there were 150 boys and 125 girls. So, the ratio of girls to boys was 125:150 = 5:6 or 5/6.
A nice way to answer this question is to pick easy-to-use numbers. Assume that in 1990 there were 200 boys and 100 girls who earned varsity letters. Then in 2000, there were 150 boys and 125 girls. So, the ratio of girls to boys was 125:150 = 5:6 or 5/6.
