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 Leauge 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 Leauge?  
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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 Leauge is <math>\frac{2366}{26}=91 \Rightarrow B</math>.  
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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 ==
*[[2003 AMC 12A Problems]]
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{{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|num-b=1|num-a=3}}
  
 
[[Category:Introductory Algebra Problems]]
 
[[Category:Introductory Algebra Problems]]

Revision as of 15:54, 29 July 2011

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?

$\mathrm{(A) \ } 77\qquad \mathrm{(B) \ } 91\qquad \mathrm{(C) \ } 143\qquad \mathrm{(D) \ } 182\qquad \mathrm{(E) \ } 286$

Solution

Since T-shirts cost $5$ dollars more than a pair of socks, T-shirts cost $5+4=9$ dollars.

Since each member needs $2$ pairs of socks and $2$ T-shirts, the total cost for $1$ member is $2(4+9)=26$ dollars.

Since $2366$ dollars was the cost for the club, and $26$ was the cost per member, the number of members in the League is $2366\div 26=\boxed{\mathrm{(B)}\ 91}$.

See Also

2003 AMC 10A (ProblemsAnswer KeyResources)
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 (ProblemsAnswer KeyResources)
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
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