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? | + | 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> \ | + | <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>. | ||
− | + | <cmath>\begin{align*} | |
− | < | + | x+y &= 34 \\ |
− | + | x-y &= 14 \\ | |
− | + | 2x &= 48 \\ | |
− | + | x &= 24 \\ | |
− | + | y &= \boxed{\textbf{(A) }10} \\ | |
− | + | \end{align*}</cmath> | |
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== See Also == | == See Also == | ||
− | + | {{AMC10 box|year=2006|ab=B|num-b=2|num-a=4}} | |
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− | + | [[Category:Introductory Algebra Problems]] | |
+ | {{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 points, and the Cougars won by a margin of points. How many points did the Panthers score?
Solution
Let be the number of points scored by the Cougars, and be the number of points scored by the Panthers. The problem is asking for the value of .
See Also
2006 AMC 10B (Problems • Answer Key • Resources) | ||
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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