2013 AMC 8 Problems/Problem 12: Difference between revisions
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==Problem== | ==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 | 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== | ||
First, find the amount of money one will pay for three sandals without the discount. | 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: <math>50 + 0.6 \times 50 + \frac{1}{2} \times 50 = \textdollar 105</math>. | |||
Finding the percentage yields <math>\frac{105}{150} = 70 \%</math>. | |||
To find the percent saved, we have <math>100 \% -70 \%= \boxed{\textbf{(B)}\ 30 \%}</math> | |||
==Solution 2== | |||
Step 1: Find the price of each sandal | |||
The first sandal is 50 dollars. | |||
The second sandal is (1-0.4)50 = 30 | |||
The third sandal is 1/2*5$ = 25 | |||
Step 2: Sum them up | |||
50+30+25 = 105 | |||
Step 2: Divide by 150 | |||
105/150 = 21/30 = 7/10 = 70 percent. | |||
Step 3: Subtract from 100 percent to find the amount he saved. | |||
100 percent -70 percent = B)30 percent | |||
-JasonDaGoat | |||
==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 13:47, 24 August 2025
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?
Solution
First, find the amount of money one will pay for three sandals without the discount. We have 
.
Then, find the amount of money using the discount: 
.
Finding the percentage yields 
.
To find the percent saved, we have 
Solution 2
Step 1: Find the price of each sandal The first sandal is 50 dollars. The second sandal is (1-0.4)50 = 30 The third sandal is 1/2*5$ = 25 Step 2: Sum them up 50+30+25 = 105 Step 2: Divide by 150 105/150 = 21/30 = 7/10 = 70 percent. Step 3: Subtract from 100 percent to find the amount he saved. 100 percent -70 percent = B)30 percent
-JasonDaGoat
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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