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

m (Solution)
m (Solution)
Line 5: Line 5:
  
 
==Solution==
 
==Solution==
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>.
+
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>.
  
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>.
+
Then, find the amount of money using the discount: <math>50 + 0.6 \time 50 + \frac{1}{2} \times 50 = \textdollar 105</math>.
  
To find the percentage of the regular, do this: <math>\frac{105}{150}</math> = <math>70 \%</math>.
+
Finding the percentage yields <math>\frac{105}{150} = 70 \%</math>.
  
To find the percent saved, do this: <math>100 \%</math> - <math>70 \%</math> = <math>\boxed{\textbf{(B)}\ 30}</math>
+
To find the percent saved, we have <math>100 \% -70 \%= \boxed{\textbf{(B)}\ 30}</math>
  
 
==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}}

Revision as of 20:17, 27 November 2013

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: $50 + 0.6 \time 50 + \frac{1}{2} \times 50 = \textdollar 105$.

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

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

See Also

2013 AMC 8 (ProblemsAnswer KeyResources)
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

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

Invalid username
Login to AoPS