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Difference between revisions of "1953 AHSME Problems/Problem 16"

(Created page with "==Problem 16== Adams plans a profit of <math>10</math> % on the selling price of an article and his expenses are <math>15</math> % of sales. The rate of markup on an article...")
 
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==Problem 16==
 
==Problem 16==
  
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Adams plans a profit of <math>10</math> % on the selling price of an article and his expenses are <math>15</math> % of sales. The rate of markup on an article that sells for \$ <math>5.00</math> is:  
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Adams plans a profit of <math>10\%</math> on the selling price of an article and his expenses are <math>15\%</math> of sales. The rate of markup on an article that sells for <math>\$5.00</math> is:  
  
 
<math>\textbf{(A)}\ 20\% \qquad
 
<math>\textbf{(A)}\ 20\% \qquad
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==Solution==
 
==Solution==
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Let the cost of the product be C, and the selling price be S. Since Adams wants a 10% profit on the sale, and his expenses are 15% of the sale, we add <math>0.10S</math> and <math>0.15S</math> to the cost to get the selling price.
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Then, <math>S=C+0.15S+0.10S \Rightarrow 0.75S=C \Rightarrow S=\frac{4}{3}C \Rightarrow \fbox{D}</math>.
  
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==See Also==
 
{{AHSME 50p box|year=1953|num-b=15|num-a=17}}
 
{{AHSME 50p box|year=1953|num-b=15|num-a=17}}
  
 
[[Category:Introductory Algebra Problems]]
 
[[Category:Introductory Algebra Problems]]
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 23:05, 30 October 2024

Problem 16

Adams plans a profit of $10\%$ on the selling price of an article and his expenses are $15\%$ of sales. The rate of markup on an article that sells for $$5.00$ is:

$\textbf{(A)}\ 20\% \qquad \textbf{(B)}\ 25\% \qquad \textbf{(C)}\ 30\% \qquad \textbf{(D)}\ 33\frac {1}{3}\% \qquad \textbf{(E)}\ 35\%$

Solution

Let the cost of the product be C, and the selling price be S. Since Adams wants a 10% profit on the sale, and his expenses are 15% of the sale, we add $0.10S$ and $0.15S$ to the cost to get the selling price. Then, $S=C+0.15S+0.10S \Rightarrow 0.75S=C \Rightarrow S=\frac{4}{3}C \Rightarrow \fbox{D}$.

See Also

1953 AHSC (Problems • Answer Key • Resources)
Preceded by
Problem 15 		Followed by
Problem 17
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All AHSME Problems and Solutions

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