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Difference between revisions of "2003 AMC 10B Problems/Problem 2"

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==Problem==
 
==Problem==
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Al gets the disease algebritis and must take one green pill and one pink pill each day for two weeks. A green pill costs <math> \ </math><math>1</math> more than a pink pill, and Al's pills cost a total of <math> \ </math><math>546</math> for the two weeks. How much does one green pill cost?
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Al gets the disease algebritis and must take one green pill and one pink pill each day for two weeks. A green pill costs <math> \ </math><math>1</math> more than a pink pill, and Al's pills cost a total of <math>\textdollar 546</math> for the two weeks. How much does one green pill cost?
  
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<math> \textbf{(A) }\ </math><math>7 \qquad\textbf{(B) }\ </math> <math>14 \qquad\textbf{(C) }\ </math><math>19\qquad\textbf{(D) }\ </math> <math>20\qquad\textbf{(E) }\ </math><math>39 </math>
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<math> \textbf{(A)}\ \textdollar 7 \qquad\textbf{(B) }\textdollar 14 \qquad\textbf{(C) }\textdollar 19\qquad\textbf{(D) }\textdollar 20\qquad\textbf{(E) }\textdollar 39 </math>
  
 
==Solution==
 
==Solution==
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x&=20\end{align*}</cmath>
 
x&=20\end{align*}</cmath>
  
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Therefore, the cost of a green pill is <math>\boxed{\textbf{(D) } 20 \text{ dollars}}</math>.
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Therefore, the cost of a green pill is <math>\boxed{\textbf{(D) }\textdollar  20}</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 18:38, 26 November 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 $\textdollar 546$ for the two weeks. How much does one green pill cost?

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

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 $\boxed{\textbf{(D) }\textdollar 20}$.

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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