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

Revision as of 20:58, 23 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 $y$ . $$ (Error compiling LaTeX. Unknown error_msg)\begin{align*} x+y &= 34 \\ x-y &= 14 \\ 2x &= 48 \\ x &= 24 \\ The answer is $(A) 10$

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 $p = 10$ .

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

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@@ Line 19: / Line 19: @@
 <math>p = 10</math>.
-p &= \boxed{\textbf{(A) }10} \\
-\end{align*}<math></math>
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Difference between revisions of "2006 AMC 10B Problems/Problem 3"

Revision as of 20:58, 23 February 2025

Contents

Problem

Solution

Solution 2

See Also