Difference between revisions of "2003 AMC 12B Problems/Problem 2"
Danielguo94 (talk | contribs) (Created page with 'Which of the following is the same as <math>(2 - 4 + 6 - 8 + 10 - 12 + 14)/ (3 - 6 + 9 - 12 + 15 - 18 + 21)</math> ? (A) <math>-1</math> (B) $- 2 3 (C) 2 3 (D) 1 (E) 14 3') |
(→Solution) |
||
| (4 intermediate revisions by 4 users not shown) | |||
| Line 1: | Line 1: | ||
| − | + | {{duplicate|[[2003 AMC 12B Problems|2003 AMC 12B #2]] and [[2003 AMC 10B Problems|2003 AMC 10B #2]]}} | |
| − | <math>( | + | |
| − | ( | + | ==Problem== |
| − | + | Al gets the disease algebritis and must take one green pill and one pink pill each day for two weeks. A green pill costs <math> \ </math><math>1</math> more than a pink pill, and Al's pills cost a total of <math>\textdollar 546</math> for the two weeks. How much does one green pill cost? | |
| − | + | ||
| − | + | <math> \textbf{(A)}\ \textdollar 7 \qquad\textbf{(B) }\textdollar 14 \qquad\textbf{(C) }\textdollar 19\qquad\textbf{(D) }\textdollar 20\qquad\textbf{(E) }\textdollar 39 </math> | |
| − | + | ||
| − | + | ==Solution== | |
| − | + | ||
| − | 3 | + | Because there are <math>14</math> days in two weeks, Al spends <math>546/14 = 39</math> dollars per day for the cost of a green pill and a pink pill. If the green pill costs <math>x</math> dollars and the pink pill <math>x-1</math> dollars, the sum of the two costs <math>2x-1</math> should equal <math>39</math> dollars. Then the cost of the green pill <math>x</math> is <math>\boxed{\textbf{(D) }\textdollar 20}</math>. |
| − | + | ||
| − | + | ==See Also== | |
| − | + | {{AMC12 box|year=2003|ab=B|num-b=1|num-a=3}} | |
| + | {{AMC10 box|year=2003|ab=B|num-b=1|num-a=3}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 16:40, 1 August 2021
- The following problem is from both the 2003 AMC 12B #2 and 2003 AMC 10B #2, so both problems redirect to this page.
Problem
Al gets the disease algebritis and must take one green pill and one pink pill each day for two weeks. A green pill costs 
more than a pink pill, and Al's pills cost a total of 
for the two weeks. How much does one green pill cost?
Solution
Because there are 
days in two weeks, Al spends 
dollars per day for the cost of a green pill and a pink pill. If the green pill costs 
dollars and the pink pill 
dollars, the sum of the two costs 
should equal 
dollars. Then the cost of the green pill is 
.
See Also
| 2003 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 1 |
Followed by Problem 3 |
| 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 | |
| 2003 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
