Difference between revisions of "2006 AMC 10B Problems/Problem 3"

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== Problem ==
 
== Problem ==
A football game was played between two teams, the Cougars and the Panthers. The two teams scored a total of 34 points, and the Cougars won by a margin of 14 points. How many points did the Panthers score?  
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A football game was played between two teams, the Cougars and the Panthers. The two teams scored a total of <math>34</math> points, and the Cougars won by a margin of <math>14</math> points. How many points did the Panthers score?  
  
<math> \mathrm{(A) \ } 10\qquad \mathrm{(B) \ } 14\qquad \mathrm{(C) \ } 17\qquad \mathrm{(D) \ } 20\qquad \mathrm{(E) \ } 24 </math>
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<math> \textbf{(A) } 10\qquad \textbf{(B) } 14\qquad \textbf{(C) } 17\qquad \textbf{(D) } 20\qquad \textbf{(E) } 24 </math>
  
 
== Solution ==
 
== Solution ==
 
Let <math>x</math> be the number of points scored by the Cougars, and <math>y</math> be the number of points scored by the Panthers. The problem is asking for the value of <math>y</math>.  
 
Let <math>x</math> be the number of points scored by the Cougars, and <math>y</math> be the number of points scored by the Panthers. The problem is asking for the value of <math>y</math>.  
 
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<cmath>\begin{align*}
<math>x+y=34</math>
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x+y &= 34 \\
 
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x-y &= 14 \\
<math>x-y=14</math>
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2x &= 48 \\
 
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x &= 24 \\
<math>2x=48</math>
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y &= \boxed{\textbf{(A) }10} \\
 
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\end{align*}</cmath>
<math>x=24</math>
 
 
 
<math>y=10 \Rightarrow A</math>
 
  
 
== See Also ==
 
== See Also ==
*[[2006 AMC 10B Problems]]
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{{AMC10 box|year=2006|ab=B|num-b=2|num-a=4}}
 
 
*[[2006 AMC 10B Problems/Problem |Previous Problem]]
 
  
*[[2006 AMC 10B Problems/Problem |Next Problem]]
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[[Category:Introductory Algebra Problems]]
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{{MAA Notice}}

Latest revision as of 10:41, 19 December 2021

Problem

A football game was played between two teams, the Cougars and the Panthers. The two teams scored a total of $34$ points, and the Cougars won by a margin of $14$ points. How many points did the Panthers score?

$\textbf{(A) } 10\qquad \textbf{(B) } 14\qquad \textbf{(C) } 17\qquad \textbf{(D) } 20\qquad \textbf{(E) } 24$

Solution

Let $x$ be the number of points scored by the Cougars, and $y$ be the number of points scored by the Panthers. The problem is asking for the value of $y$. \begin{align*} x+y &= 34 \\ x-y &= 14 \\ 2x &= 48 \\ x &= 24 \\ y &= \boxed{\textbf{(A) }10} \\ \end{align*}

See Also

2006 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 2
Followed by
Problem 4
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

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