Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

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

(Created page with "== Problem == A farmer bought <math>749</math> sheep. He sold <math>700</math> of them for the price paid for the <math>749</math> sheep. The remaining <math>49</math> sheep...")
 
(→‎Solution)
Line 15: Line 15:
 
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>.
  
−
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>\box{\textbf{(C)}}</math>
+
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==

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
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
All AHSME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1964_AHSME_Problems/Problem_14&oldid=107840"