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Difference between revisions of "1955 AHSME Problems/Problem 5"

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== Problem ==
 
== Problem ==
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<math>5y</math> varies inversely as the square of <math>x</math>. When <math>y=16, x=1</math>. When <math>x=8, y</math> equals:
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<math>\textbf{(A)}\ 2 \qquad \textbf{(B)}\ 128 \qquad \textbf{(C)}\ 64 \qquad \textbf{(D)}\ \frac{1}{4} \qquad \textbf{(E)}\ 1024    </math>
  
 
==Solution==
 
==Solution==
 +
An inverse variation can be expressed in the form <math>xy = n</math>, where <math>n</math> is any number (except perhaps zero). Since <math>5y</math> varies inversely with the square of <math>x</math>, this particular one will be <math>5yx^2 = n</math>.
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We can plug in <math>16</math> for <math>y</math> and <math>1</math> for <math>x</math>, which makes <math>n=80</math>. The equation is now <math>5yx^2 = 80</math>.
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When <math>x = 8</math>, we can solve for <math>y</math> using the equation <math>320y = 80</math>, which makes <math>y</math> <math>\boxed{\textbf{(D)} \frac{1}{4}}</math>.
  
 
==See Also==
 
==See Also==
  
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{{AHSME 50p box|year=1955|num-b=|num-a=}}
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{{AHSME 50p box|year=1955|num-b=4|num-a=6}}
  
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 00:52, 14 October 2021

Problem

$5y$ varies inversely as the square of $x$. When $y=16, x=1$. When $x=8, y$ equals:

$\textbf{(A)}\ 2 \qquad \textbf{(B)}\ 128 \qquad \textbf{(C)}\ 64 \qquad \textbf{(D)}\ \frac{1}{4} \qquad \textbf{(E)}\ 1024$

Solution

An inverse variation can be expressed in the form $xy = n$, where $n$ is any number (except perhaps zero). Since $5y$ varies inversely with the square of $x$, this particular one will be $5yx^2 = n$.

We can plug in $16$ for $y$ and $1$ for $x$, which makes $n=80$. The equation is now $5yx^2 = 80$.

When $x = 8$, we can solve for $y$ using the equation $320y = 80$, which makes $y$ $\boxed{\textbf{(D)} \frac{1}{4}}$.

See Also

1955 AHSC (Problems • Answer Key • Resources)
Preceded by
Problem 4 		Followed by
Problem 6
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 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50
All AHSME Problems and Solutions


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