Difference between revisions of "2014 AMC 10A Problems/Problem 11"
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\textbf{(E) }\textdollar259.95\qquad</math> | \textbf{(E) }\textdollar259.95\qquad</math> | ||
| − | ==Solution== | + | ==Solution 1== |
Let the listed price be <math>x</math>. Since all the answer choices are above <math>\textdollar100</math>, we can assume <math>x > 100</math>. Thus the prices after coupons will be as follows: | Let the listed price be <math>x</math>. Since all the answer choices are above <math>\textdollar100</math>, we can assume <math>x > 100</math>. Thus the prices after coupons will be as follows: | ||
| Line 35: | Line 35: | ||
The only answer choice that satisfies these constraints is <math>\boxed{\textbf{(C) }\textdollar219.95}</math> | The only answer choice that satisfies these constraints is <math>\boxed{\textbf{(C) }\textdollar219.95}</math> | ||
| + | |||
| + | ==Solution 2: Using the Answer Choices== | ||
| + | When you look at the answer choices, you know that we can immediately take out A and B because when you take of <math>20 twenty from them, it is more than 10%. We know C is the right answer because it is the first one that is larger than </math>200, which is the line in which taking off $20 is less than 20%. | ||
| + | |||
| + | (Solution by William Chi) | ||
==See Also== | ==See Also== | ||
Revision as of 13:14, 9 February 2014
- The following problem is from both the 2014 AMC 12A #8 and 2014 AMC 10A #11, so both problems redirect to this page.
Problem
A customer who intends to purchase an appliance has three coupons, only one of which may be used:
Coupon 1: 
off the listed price if the listed price is at least 
Coupon 2: 
off the listed price if the listed price is at least 
Coupon 3: 
off the amount by which the listed price exceeds
For which of the following listed prices will coupon 
offer a greater price reduction than either coupon 
or coupon 
?
Solution 1
Let the listed price be 
. Since all the answer choices are above , we can assume 
. Thus the prices after coupons will be as follows:
Coupon 1: 
Coupon 2: 
Coupon 3: 
For coupon to give a better price reduction than the other coupons, we must have 
and 
.
From the first inequality, 
.
From the second inequality, 
.
The only answer choice that satisfies these constraints is 
Solution 2: Using the Answer Choices
When you look at the answer choices, you know that we can immediately take out A and B because when you take of $20 twenty from them, it is more than 10%. We know C is the right answer because it is the first one that is larger than$ (Error compiling LaTeX. Unknown error_msg)200, which is the line in which taking off $20 is less than 20%.
(Solution by William Chi)
See Also
| 2014 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 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 AMC 10 Problems and Solutions | ||
| 2014 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 7 |
Followed by Problem 9 |
| 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 AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
