Difference between revisions of "2006 AMC 10B Problems/Problem 3"
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x-y &= 14 \\ | x-y &= 14 \\ | ||
2x &= 48 \\ | 2x &= 48 \\ | ||
| − | x &= 24 \\ | + | x &= 24 \\$<math> |
| − | The answer is <math>\boxed{\textbf{(A) } 10}< | + | The answer is </math>\boxed{\textbf{(A) } 10}<math> |
== Solution 2 == | == Solution 2 == | ||
| − | <math>c< | + | </math>c<math> is the amount the Cougars scored and </math>p<math> is the score for Panthers. Since the Cougars won by 14 points, </math>c = p + 14<math>. Using substitution, |
| − | <math>2p + 14 = 34< | + | </math>2p + 14 = 34<math>, |
| − | <math>2p = 20< | + | </math>2p = 20<math>, and then |
| − | <math>p = 10< | + | </math>p = 10<math>. |
p &= \boxed{\textbf{(A) }10} \\ | p &= \boxed{\textbf{(A) }10} \\ | ||
| − | \end{align*} | + | \end{align*}</math>$ |
-- leafy | -- leafy | ||
Revision as of 09:29, 24 February 2025
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 .
$$ (Error compiling LaTeX. Unknown error_msg)\begin{align*}
x+y &= 34 \\
x-y &= 14 \\
2x &= 48 \\
x &= 24 \$
\boxed{\textbf{(A) } 10}
c
p
c = p + 14
2p + 14 = 34
2p = 20
p = 10$.
p &= \boxed{\textbf{(A) }10} \\ \end{align*}$ (Error compiling LaTeX. Unknown error_msg)$
-- leafy
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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
