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Difference between revisions of "1951 AHSME Problems/Problem 5"

(New page: Mr.<math>A</math> earns <math>1.1\cdot10,000=11,000</math> dollars after he sells it to Mr. <math>B</math>. Then, Mr. <math>B</math> sells it at a price of <math>(1-0.1)\cdot11,000=9,900</...)
 
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Mr.<math>A</math> earns <math>1.1\cdot10,000=11,000</math> dollars after he sells it to Mr. <math>B</math>. Then, Mr. <math>B</math> sells it at a price of <math>(1-0.1)\cdot11,000=9,900</math> collars, so Mr. <math>A</math> ultimately earns <math>1,100</math> dollars <math>\implies\boxed D</math>.
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== Problem 5 ==
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Mr. <math>A</math> owns a home worth <math>\</math>10,000.  He sells it to Mr. <math>B</math> at a 10% profit based on the worth of the house. Mr. <math>B</math> sells the house back to Mr. <math>A</math> at a 10% loss.  Then:
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<math> \mathrm{(A) \ A\ comes\ out\ even  } \qquad</math> <math>\mathrm{(B) \ A\ makes\ 1100\ on\ the\ deal}</math> <math> \qquad \mathrm{(C) \ A\ makes\ 1000\ on\ the\ deal } \qquad</math> <math>\mathrm{(D) \ A\ loses\ 900\ on\ the\ deal }</math> <math>\qquad \mathrm{(E) \ A\ loses\ 1000\ on\ the\ deal }  </math>
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==Solution==
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Mr.<math>A</math> earns <math>1.1\cdot</math><dollar/><math>10,000=</math><dollar/><math>11,000</math> after he sells it to Mr. <math>B</math>. Then, Mr. <math>B</math> sells it at a price of <math>(1-0.1)\cdot</math><dollar/><math>11,000=</math><dollar/><math>9,900</math>, so Mr. <math>A</math> ultimately earns <math>\boxed{\textbf{(D)}}</math><dollar/><math>1,100</math>.

Revision as of 15:04, 1 February 2009

Problem 5

Mr. $A$ owns a home worth $$10,000. He sells it to Mr. $B$ at a 10% profit based on the worth of the house. Mr. $B$ sells the house back to Mr. $A$ at a 10% loss. Then:

$\mathrm{(A) \ A\ comes\ out\ even } \qquad$ $\mathrm{(B) \ A\ makes\ 1100\ on\ the\ deal}$ $\qquad \mathrm{(C) \ A\ makes\ 1000\ on\ the\ deal } \qquad$ $\mathrm{(D) \ A\ loses\ 900\ on\ the\ deal }$ $\qquad \mathrm{(E) \ A\ loses\ 1000\ on\ the\ deal }$

Solution

Mr.$A$ earns $1.1\cdot$<dollar/>$10,000=$<dollar/>$11,000$ after he sells it to Mr. $B$. Then, Mr. $B$ sells it at a price of $(1-0.1)\cdot$<dollar/>$11,000=$<dollar/>$9,900$, so Mr. $A$ ultimately earns $\boxed{\textbf{(D)}}$<dollar/>$1,100$.

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