Difference between revisions of "2000 AMC 10 Problems/Problem 8"

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Let <math>f</math> be the number of freshman and s be the number of sophomores.
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==Problem==
  
<math>\frac{2}{5}f=\frac{4}{5}s</math>.
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At Olympic High School, <math>\frac{2}{5}</math> of the freshmen and <math>\frac{4}{5}</math> of the sophomores took the AMC-10. Given that the number of freshmen and sophomore contestants was the same, which of the following must be true?
<math>f=2s</math>.
 
  
There are twice as many freshman as sophomores.
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<math>\mathrm{(A)}</math> There are five times as many sophomores as freshmen.
D.
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<math>\mathrm{(B)}</math> There are twice as many sophomores as freshmen.
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<math>\mathrm{(C)}</math> There are as many freshmen as sophomores.
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<math>\mathrm{(D)}</math> There are twice as many freshmen as sophomores.
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<math>\mathrm{(E)}</math> There are five times as many freshmen as sophomores.
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==Solution==
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Let <math>f</math> be the number of freshman and <math>s</math> be the number of sophomores.
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<math>\frac{2}{5}f=\frac{4}{5}s</math>
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<math>2f = 4s</math>
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<math>f=2s</math>
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There are twice as many freshmen as sophomores.
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<math>\boxed{\text{D}}</math>
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==See Also==
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{{AMC10 box|year=2000|num-b=7|num-a=9}}
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{{MAA Notice}}
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[[Category:Introductory Algebra Problems]]
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[[Category:Introductory Number Theory Problems]]

Latest revision as of 15:36, 19 April 2021

Problem

At Olympic High School, $\frac{2}{5}$ of the freshmen and $\frac{4}{5}$ of the sophomores took the AMC-10. Given that the number of freshmen and sophomore contestants was the same, which of the following must be true?

$\mathrm{(A)}$ There are five times as many sophomores as freshmen.

$\mathrm{(B)}$ There are twice as many sophomores as freshmen.

$\mathrm{(C)}$ There are as many freshmen as sophomores.

$\mathrm{(D)}$ There are twice as many freshmen as sophomores.

$\mathrm{(E)}$ There are five times as many freshmen as sophomores.

Solution

Let $f$ be the number of freshman and $s$ be the number of sophomores.

$\frac{2}{5}f=\frac{4}{5}s$

$2f = 4s$

$f=2s$

There are twice as many freshmen as sophomores. $\boxed{\text{D}}$

See Also

2000 AMC 10 (ProblemsAnswer KeyResources)
Preceded by
Problem 7
Followed by
Problem 9
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 10 Problems and Solutions

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