1959 AHSME Problems/Problem 9: Difference between revisions
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== Problem == | |||
A farmer divides his herd of <math>n</math>cows among his four sons so that one son gets one-half the herd, a second son, one-fourth, a third son, one-fifth, and the fourth son, <math>7</math> cows. Then <math>n</math> is: <math>\textbf{(A)}\ 80 \qquad\textbf{(B)}\ 100\qquad\textbf{(C)}\ 140\qquad\textbf{(D)}\ 180\qquad\textbf{(E)}\ 240</math> | A farmer divides his herd of <math>n</math>cows among his four sons so that one son gets one-half the herd, a second son, one-fourth, a third son, one-fifth, and the fourth son, <math>7</math> cows. Then <math>n</math> is: <math>\textbf{(A)}\ 80 \qquad\textbf{(B)}\ 100\qquad\textbf{(C)}\ 140\qquad\textbf{(D)}\ 180\qquad\textbf{(E)}\ 240</math> | ||
==Solution== | == Solution == | ||
The first three sons get <math>\frac{1}{2}+\frac{1}{4}+\frac{1}{5}=\frac{19}{20}</math> of the herd, so that the fourth son should get <math>\frac{1}{20}</math> of it. But the fourth son gets <math>7</math> cows, so the size of the herd is <math>n=\frac{7}{\frac{1}{20}} = 140</math>. Then our answer is <math>\boxed{C}</math>, and we are done. | The first three sons get <math>\frac{1}{2}+\frac{1}{4}+\frac{1}{5}=\frac{19}{20}</math> of the herd, so that the fourth son should get <math>\frac{1}{20}</math> of it. But the fourth son gets <math>7</math> cows, so the size of the herd is <math>n=\frac{7}{\frac{1}{20}} = 140</math>. Then our answer is <math>\boxed{C}</math>, and we are done. | ||
Revision as of 12:57, 16 July 2024
Problem
A farmer divides his herd of 
cows among his four sons so that one son gets one-half the herd, a second son, one-fourth, a third son, one-fifth, and the fourth son, 
cows. Then is: 
Solution
The first three sons get 
of the herd, so that the fourth son should get 
of it. But the fourth son gets cows, so the size of the herd is 
. Then our answer is 
, and we are done.
