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Difference between revisions of "2013 AMC 8 Problems/Problem 12"

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==Problem==
 
==Problem==
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At the 2013 Winnebago County Fair a vendor is offering a "fair special" on sandals. If you buy one pair of sandals at the regular price of $50, you get a second pair at a 40% discount, and a third pair at half the regular price. Javier took advantage of the "fair special" to buy three pairs of sandals. What percentage of the $150 regular price did he save?
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At the 2013 Winnebago County Fair a vendor is offering a "fair special" on sandals. If you buy one pair of sandals at the regular price of \$50, you get a second pair at a 40% discount, and a third pair at half the regular price. Javier took advantage of the "fair special" to buy three pairs of sandals. What percentage of the \$150 regular price did he save?
  
 
<math>\textbf{(A)}\ 25 \qquad \textbf{(B)}\ 30 \qquad \textbf{(C)}\ 33 \qquad \textbf{(D)}\ 40 \qquad \textbf{(E)}\ 45</math>
 
<math>\textbf{(A)}\ 25 \qquad \textbf{(B)}\ 30 \qquad \textbf{(C)}\ 33 \qquad \textbf{(D)}\ 40 \qquad \textbf{(E)}\ 45</math>
  
 
==Solution==
 
==Solution==
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First, find the amount of money one will pay for three sandals without the discount. This would = the regular price, <math>\textdollar 50</math> <math>\times</math> 3 sandals = <math>\textdollar 150</math>.
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First, find the amount of money one will pay for three sandals without the discount. We have <math>\textdollar 50\times 3 \text{ sandals} = \textdollar 150</math>.
  
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Then, find the amount of money using the discount: 50 + 0.6 <math>\times</math> 50 + <math>\frac{1}{2}</math> <math>\times</math> 50 = <math>\textdollar 105</math>.
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Then, find the amount of money using the discount: <math>50 + 0.6 \times 50 + \frac{1}{2} \times 50 = \textdollar 105</math>.
  
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To find the percentage of the regular, do this: <math>\frac{105}{150}</math> = <math>70 \%</math>.
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Finding the percentage yields <math>\frac{105}{150} = 70 \%</math>.
  
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To find the percent saved, do this: <math>100 \%</math> - <math>70 \%</math> = <math>\boxed{\textbf{(B)}\ 30}</math>
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To find the percent saved, we have <math>100 \% -70 \%= \boxed{\textbf{(B)}\ 30 \%}</math>
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 +
==Video Solution==
 +
https://youtu.be/VQPKh5hc3xY ~savannahsolver
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2013|num-b=11|num-a=13}}
 
{{AMC8 box|year=2013|num-b=11|num-a=13}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 09:20, 16 November 2024

Problem

At the 2013 Winnebago County Fair a vendor is offering a "fair special" on sandals. If you buy one pair of sandals at the regular price of $50, you get a second pair at a 40% discount, and a third pair at half the regular price. Javier took advantage of the "fair special" to buy three pairs of sandals. What percentage of the $150 regular price did he save?

$\textbf{(A)}\ 25 \qquad \textbf{(B)}\ 30 \qquad \textbf{(C)}\ 33 \qquad \textbf{(D)}\ 40 \qquad \textbf{(E)}\ 45$

Solution

First, find the amount of money one will pay for three sandals without the discount. We have $\textdollar 50\times 3 \text{ sandals} = \textdollar 150$.

Then, find the amount of money using the discount: $50 + 0.6 \times 50 + \frac{1}{2} \times 50 = \textdollar 105$.

Finding the percentage yields $\frac{105}{150} = 70 \%$.

To find the percent saved, we have $100 \% -70 \%= \boxed{\textbf{(B)}\ 30 \%}$

Video Solution

https://youtu.be/VQPKh5hc3xY ~savannahsolver

See Also

2013 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 11 		Followed by
Problem 13
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
All AJHSME/AMC 8 Problems and Solutions

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