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Difference between revisions of "1964 AHSME Problems/Problem 14"

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Let us say each sheep cost <math>x</math> dollars.  The farmer paid <math>749x</math> for the sheep.  He sold <math>700</math> of them for <math>749x</math>, so each sheep sold for <math>\frac{749}{700} = 1.07x</math>.
 
Let us say each sheep cost <math>x</math> dollars.  The farmer paid <math>749x</math> for the sheep.  He sold <math>700</math> of them for <math>749x</math>, so each sheep sold for <math>\frac{749}{700} = 1.07x</math>.
  
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Since every sheep sold for the same price per head, and since every sheep cost <math>x</math> and sold for <math>1.07x</math>, there is an increase of <math>\frac{1.07x - 1x}{1x} = 0.07</math>, or <math>7\%</math>, which is option <math>\boxed{\textbf{(C}}</math>
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Since every sheep sold for the same price per head, and since every sheep cost <math>x</math> and sold for <math>1.07x</math>, there is an increase of <math>\frac{1.07x - 1x}{1x} = 0.07</math>, or <math>7\%</math>, which is option <math>\boxed{\textbf{(C)}}</math>
  
 
==See Also==
 
==See Also==

Latest revision as of 17:33, 23 July 2019

Problem

A farmer bought $749$ sheep. He sold $700$ of them for the price paid for the $749$ sheep. The remaining $49$ sheep were sold at the same price per head as the other $700$. Based on the cost, the percent gain on the entire transaction is:

$\textbf{(A)}\ 6.5 \qquad \textbf{(B)}\ 6.75 \qquad \textbf{(C)}\ 7 \qquad \textbf{(D)}\ 7.5 \qquad \textbf{(E)}\ 8$

Solution

Let us say each sheep cost $x$ dollars. The farmer paid $749x$ for the sheep. He sold $700$ of them for $749x$, so each sheep sold for $\frac{749}{700} = 1.07x$.

Since every sheep sold for the same price per head, and since every sheep cost $x$ and sold for $1.07x$, there is an increase of $\frac{1.07x - 1x}{1x} = 0.07$, or $7\%$, which is option $\boxed{\textbf{(C)}}$

See Also

1964 AHSC (Problems • Answer Key • Resources)
Preceded by
Problem 13 		Followed by
Problem 15
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All AHSME Problems and Solutions

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