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

 
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== Problem ==
 
== Problem ==
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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?
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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>
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== Solution ==
 
== Solution ==
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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*}
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x+y &= 34 \\
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x-y &= 14 \\
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2x &= 48 \\
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x &= 24 \\
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y &= \boxed{\textbf{(A) }10} \\
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\end{align*}</cmath>
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== See Also ==
 
== See Also ==
*[[2006 AMC 10B Problems]]
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{{AMC10 box|year=2006|ab=B|num-b=2|num-a=4}}
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[[Category:Introductory Algebra Problems]]
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{{MAA Notice}}

Latest revision as of 09:41, 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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