2006 AMC 10B Problems/Problem 3: Difference between revisions

Latest revision as of 09:31, 24 February 2025

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 $y$ . $\begin{align*} x+y &= 34 \\ x-y &= 14 \\ 2x &= 48 \\ x &= 24 \\ \end{align*}$ The answer is $\boxed{\textbf{(A) } 10}$

Solution 2

$c$ is the amount the Cougars scored and $p$ is the score for Panthers. Since the Cougars won by 14 points, $c = p + 14$ . Using substitution, $2p + 14 = 34$ , $2p = 20$ , and then $p = 10$ .

$\begin{align*} p &= \boxed{\textbf{(A) }10} \\ \end{align*}$

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2006 AMC 10B (Problems • Answer Key • Resources)
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All AMC 10 Problems and Solutions

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: File missing

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 <math>p = 10</math>.
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 p &= \boxed{\textbf{(A) }10} \\
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2006 AMC 10B Problems/Problem 3: Difference between revisions

Latest revision as of 09:31, 24 February 2025

Contents

Problem

Solution

Solution 2

See Also