2010 AMC 10B Problems/Problem 11
Contents
[hide]Problem
A shopper plans to purchase an item that has a listed price greater than and can use any one of the three coupons. Coupon A gives off the listed price, Coupon B gives off the listed price, and Coupon C gives off the amount by which the listed price exceeds
.
Let and be the smallest and largest prices, respectively, for which Coupon A saves at least as many dollars as Coupon B or C. What is ?
Solution
Let the listed price be , where
Coupon A saves us:
Coupon B saves us:
Coupon C saves us:
Now, the condition is that A has to be greater than or equal to either B or C which gives us the following inequalities:
We see here that the greatest possible value for is , thus and the smallest value for is so .
The difference between and is
Video Solution
~IceMatrix
See Also
2010 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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All AMC 10 Problems and Solutions |
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