Difference between revisions of "2002 AMC 8 Problems/Problem 14"
Mrdavid445 (talk | contribs) (→Solution #1) |
(→Solution) |
||
(9 intermediate revisions by 5 users not shown) | |||
Line 1: | Line 1: | ||
− | + | == Problem == | |
− | == Problem | ||
A merchant offers a large group of items at <math>30\%</math> off. Later, the merchant takes <math>20\%</math> off these sale prices and claims that the final price of these items is <math>50\%</math> off the original price. The total discount is | A merchant offers a large group of items at <math>30\%</math> off. Later, the merchant takes <math>20\%</math> off these sale prices and claims that the final price of these items is <math>50\%</math> off the original price. The total discount is | ||
Line 7: | Line 6: | ||
<math> \text{(A)}\ 35\%\qquad\text{(B)}\ 44\%\qquad\text{(C)}\ 50\%\qquad\text{(D)}\ 56\%\qquad\text{(E)}\ 60\% </math> | <math> \text{(A)}\ 35\%\qquad\text{(B)}\ 44\%\qquad\text{(C)}\ 50\%\qquad\text{(D)}\ 56\%\qquad\text{(E)}\ 60\% </math> | ||
− | ==Solution | + | ==Solution== |
+ | ===Solution 1=== | ||
− | Let's assume that each item is <math> | + | Let's assume that each item is <math>100</math> dollars. First we take off <math>30\%</math> off of <math>100</math> dollars. <math>100\cdot0.7=70</math> |
Next, we take off the extra <math>20\%</math> as asked by the problem. <math>70\cdot0.80=56</math> | Next, we take off the extra <math>20\%</math> as asked by the problem. <math>70\cdot0.80=56</math> | ||
− | So the final price of an item is | + | So the final price of an item is \$56. We have to do <math>100-56</math> because <math>56</math> was the final price and we wanted the discount. |
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | + | ==See Also== | |
+ | {{AMC8 box|year=2002|num-b=13|num-a=15}} | ||
+ | {{MAA Notice}} |
Latest revision as of 20:56, 29 June 2021
Contents
Problem
A merchant offers a large group of items at off. Later, the merchant takes off these sale prices and claims that the final price of these items is off the original price. The total discount is
Solution
Solution 1
Let's assume that each item is dollars. First we take off off of dollars.
Next, we take off the extra as asked by the problem.
So the final price of an item is $56. We have to do because was the final price and we wanted the discount.
See Also
2002 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.