Difference between revisions of "2014 AMC 10A Problems/Problem 11"
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The only answer choice that remains is <math>\boxed{\textbf{(C) }\textdollar219.95}</math>. | The only answer choice that remains is <math>\boxed{\textbf{(C) }\textdollar219.95}</math>. | ||
| + | |||
| + | ==Solution 2 (Using The Answers)== | ||
| + | For coupon <math>1</math> to be the most effective, we want 10\%\ of the price to be greater than 20. This clearly occurs if the value is over 200. | ||
| + | Reading Coupon 3, we want to minimize the value over 200, so <math>\textbf{(C)}</math> is the smallest number over 200. | ||
==See Also== | ==See Also== | ||
Revision as of 13:01, 23 December 2016
- 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 discounts after the coupons are used will be as follows:
Coupon 1: 
Coupon 2: 
Coupon 3: 
For coupon to give a greater price reduction than the other coupons, we must have 
and 
.
From the first inequality, the listed price must be greater than 
, so answer choices 
and 
are eliminated.
From the second inequality, the listed price must be less than 
, so answer choices 
and 
are eliminated.
The only answer choice that remains is 
.
Solution 2 (Using The Answers)
For coupon to be the most effective, we want 10\%\ of the price to be greater than 20. This clearly occurs if the value is over 200.
Reading Coupon 3, we want to minimize the value over 200, so 
is the smallest number over 200.
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. 
