2014 AMC 10A Problems/Problem 11
- 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 off 20 dollars from them, it is more than 10%. We know C is the right answer because it is the first one that is larger than 200 dollars, which is the line in which taking off 20 dollars is less than 10%.
(Solution by Flamedragon)
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.