Difference between revisions of "2003 AMC 12A Problems/Problem 2"
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| + | {{duplicate|[[2003 AMC 12A Problems|2003 AMC 12A #2]] and [[2003 AMC 10A Problems|2003 AMC 10A #2]]}} | ||
== Problem == | == Problem == | ||
| − | Members of the Rockham Soccer | + | Members of the Rockham Soccer League buy socks and T-shirts. Socks cost $4 per pair and each T-shirt costs $5 more than a pair of socks. Each member needs one pair of socks and a shirt for home games and another pair of socks and a shirt for away games. If the total cost is $2366, how many members are in the League? |
<math> \mathrm{(A) \ } 77\qquad \mathrm{(B) \ } 91\qquad \mathrm{(C) \ } 143\qquad \mathrm{(D) \ } 182\qquad \mathrm{(E) \ } 286 </math> | <math> \mathrm{(A) \ } 77\qquad \mathrm{(B) \ } 91\qquad \mathrm{(C) \ } 143\qquad \mathrm{(D) \ } 182\qquad \mathrm{(E) \ } 286 </math> | ||
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Since each member needs <math>2</math> pairs of socks and <math>2</math> T-shirts, the total cost for <math>1</math> member is <math>2(4+9)=26</math> dollars. | Since each member needs <math>2</math> pairs of socks and <math>2</math> T-shirts, the total cost for <math>1</math> member is <math>2(4+9)=26</math> dollars. | ||
| − | Since <math>2366</math> dollars was the cost for the club, and <math>26</math> was the cost per member, the number of members in the | + | Since <math>2366</math> dollars was the cost for the club, and <math>26</math> was the cost per member, the number of members in the League is <math>2366\div 26=\boxed{\mathrm{(B)}\ 91}</math>. |
== See Also == | == See Also == | ||
| − | + | {{AMC10 box|year=2003|ab=A|num-b=1|num-a=3}} | |
| − | + | {{AMC12 box|year=2003|ab=A|num-b=1|num-a=3}} | |
| − | {{AMC12 box|year=2003|ab=A| | ||
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 09:16, 4 July 2013
- The following problem is from both the 2003 AMC 12A #2 and 2003 AMC 10A #2, so both problems redirect to this page.
Problem
Members of the Rockham Soccer League buy socks and T-shirts. Socks cost $4 per pair and each T-shirt costs $5 more than a pair of socks. Each member needs one pair of socks and a shirt for home games and another pair of socks and a shirt for away games. If the total cost is $2366, how many members are in the League?
Solution
Since T-shirts cost 
dollars more than a pair of socks, T-shirts cost 
dollars.
Since each member needs 
pairs of socks and T-shirts, the total cost for 
member is 
dollars.
Since 
dollars was the cost for the club, and 
was the cost per member, the number of members in the League is 
.
See Also
| 2003 AMC 10A (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 | ||
| 2003 AMC 12A (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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
