Difference between revisions of "2006 AMC 10B Problems/Problem 3"
Math Kirby (talk | contribs) (→See Also) |
Dairyqueenxd (talk | contribs) (→Solution) |
||
| (3 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
== 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> | |
| − | |||
| − | |||
| − | |||
== See Also == | == See Also == | ||
| Line 21: | Line 18: | ||
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
| + | {{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 
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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
