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Difference between revisions of "2003 AMC 10B Problems/Problem 2"
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Line 10: Line 10:
 
Let the cost of a green pill be <math>x</math> dollars.  This makes the cost of a pink pill <math>(x-1)</math> dollars.
 
Let the cost of a green pill be <math>x</math> dollars.  This makes the cost of a pink pill <math>(x-1)</math> dollars.
  
−
Now we set up the equation and solve.  Since there are <math>14</math> pills of each color, the total cost of all pills, pink and green, is <math>14x+14(x-1)</math> dollars.  Setting this equal to <math>546</math> and solving gives us:
+
Now we set up the equation and solve.  Since there are <math>14</math> pills of each color, the total cost of all pills, pink and green, is <math>14x+14(x-1)</math> dollars.  Setting this equal to <math>546</math> and solving gives us
  
−
<math>14x+14(x-1)=546</math>
+
<cmath>\begin{align*}
 +
14x+14(x-1)&=546\\
 +
x+(x-1)&=39\\
 +
2x-1&=39\\
 +
2x&=40\\
 +
x&=20\end{align*}</cmath>
  
−
<math>x+(x-1)=39</math>
+
Therefore, the cost of a green pill is <math>\boxed{\textbf{(D) } 20 \text{ dollars}}</math>.
−
 
 
−
<math>2x-1=39</math>
 
−
 
 
−
<math>2x=40</math>
 
−
 
 
−
<math>x=20</math>
 
−
 
 
−
Therefore, the cost of a green pill is <math> \ </math><math>20</math> <math> \boxed{\textbf{(D)}}</math>.
 
  
 
==See Also==
 
==See Also==
  
 
{{AMC10 box|year=2003|ab=B|num-b=1|num-a=3}}
 
{{AMC10 box|year=2003|ab=B|num-b=1|num-a=3}}

Revision as of 02:06, 10 June 2011

Problem

Al gets the disease algebritis and must take one green pill and one pink pill each day for two weeks. A green pill costs $$$1$ more than a pink pill, and Al's pills cost a total of $$$546$ for the two weeks. How much does one green pill cost?

$\textbf{(A) }$$7 \qquad\textbf{(B) }$ $14 \qquad\textbf{(C) }$$19\qquad\textbf{(D) }$ $20\qquad\textbf{(E) }$$39$

Solution

Since there are $14$ days in $2$ weeks, Al has to take $14$ green pills and $14$ pink pills in the two week span.

Let the cost of a green pill be $x$ dollars. This makes the cost of a pink pill $(x-1)$ dollars.

Now we set up the equation and solve. Since there are $14$ pills of each color, the total cost of all pills, pink and green, is $14x+14(x-1)$ dollars. Setting this equal to $546$ and solving gives us

\begin{align*} 14x+14(x-1)&=546\\ x+(x-1)&=39\\ 2x-1&=39\\ 2x&=40\\ x&=20\end{align*}

Therefore, the cost of a green pill is $\boxed{\textbf{(D) } 20 \text{ dollars}}$.

See Also

2003 AMC 10B (Problems • Answer Key • Resources)
Preceded by
Problem 1 		Followed by
Problem 3
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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