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Difference between revisions of "2002 AMC 8 Problems/Problem 10"
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Juan organizes the stamps in his collection by country and by the decade in which they were issued. The prices he paid for them at a stamp shop were: Brazil and France, 6 cents each, Peru 4 cents each, and Spain 5 cents each. (Brazil and Peru are South American countries and France and Spain are in Europe.) The average price of his '70s stamps is closest to
 
Juan organizes the stamps in his collection by country and by the decade in which they were issued. The prices he paid for them at a stamp shop were: Brazil and France, 6 cents each, Peru 4 cents each, and Spain 5 cents each. (Brazil and Peru are South American countries and France and Spain are in Europe.) The average price of his '70s stamps is closest to
 +
 +
<asy>
 +
/* AMC8 2002 #8, 9, 10 Problem */
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size(3inch, 1.5inch);
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for ( int y = 0; y <= 5; ++y )
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{
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draw((0,y)--(18,y));
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}
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draw((0,0)--(0,5));
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draw((6,0)--(6,5));
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draw((9,0)--(9,5));
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draw((12,0)--(12,5));
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draw((15,0)--(15,5));
 +
draw((18,0)--(18,5));
 +
draw(scale(0.8)*"50s", (7.5,4.5));
 +
draw(scale(0.8)*"4", (7.5,3.5));
 +
draw(scale(0.8)*"8", (7.5,2.5));
 +
draw(scale(0.8)*"6", (7.5,1.5));
 +
draw(scale(0.8)*"3", (7.5,0.5));
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draw(scale(0.8)*"60s", (10.5,4.5));
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draw(scale(0.8)*"7", (10.5,3.5));
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draw(scale(0.8)*"4", (10.5,2.5));
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draw(scale(0.8)*"4", (10.5,1.5));
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draw(scale(0.8)*"9", (10.5,0.5));
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draw(scale(0.8)*"70s", (13.5,4.5));
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draw(scale(0.8)*"12", (13.5,3.5));
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draw(scale(0.8)*"12", (13.5,2.5));
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draw(scale(0.8)*"6", (13.5,1.5));
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draw(scale(0.8)*"13", (13.5,0.5));
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draw(scale(0.8)*"80s", (16.5,4.5));
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draw(scale(0.8)*"8", (16.5,3.5));
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draw(scale(0.8)*"15", (16.5,2.5));
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draw(scale(0.8)*"10", (16.5,1.5));
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draw(scale(0.8)*"9", (16.5,0.5));
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label(scale(0.8)*"Country", (3,4.5));
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label(scale(0.8)*"Brazil", (3,3.5));
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label(scale(0.8)*"France", (3,2.5));
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label(scale(0.8)*"Peru", (3,1.5));
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label(scale(0.8)*"Spain", (3,0.5));
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label(scale(0.9)*"Juan's Stamp Collection", (9,0), S);
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label(scale(0.9)*"Number of Stamps by Decade", (9,5), N);</asy>
  
  
 
<math> \text{(A)}\ 3.5\text{ cents}\qquad\text{(B)}\ 4\text{ cents}\qquad\text{(C)}\ 4.5\text{ cents}\qquad\text{(D)}\ 5\text{ cents}\qquad\text{(E)}\ 5.5\text{ cents} </math>
 
<math> \text{(A)}\ 3.5\text{ cents}\qquad\text{(B)}\ 4\text{ cents}\qquad\text{(C)}\ 4.5\text{ cents}\qquad\text{(D)}\ 5\text{ cents}\qquad\text{(E)}\ 5.5\text{ cents} </math>
 +
 +
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==Solution==
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<math>12*0.06*2=1.44</math>
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 +
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<math>6*0.04=0.24</math>
 +
 +
<math>13*0.05=0.65</math>
 +
 +
Sum is <math>2.33</math>
 +
 +
Total there are <math>43</math> stamps
 +
 +
<math>2.33/43=</math> <math>\boxed{E}</math>

Revision as of 15:34, 8 January 2012

Problem 10

Juan organizes the stamps in his collection by country and by the decade in which they were issued. The prices he paid for them at a stamp shop were: Brazil and France, 6 cents each, Peru 4 cents each, and Spain 5 cents each. (Brazil and Peru are South American countries and France and Spain are in Europe.) The average price of his '70s stamps is closest to

[asy] /* AMC8 2002 #8, 9, 10 Problem */ size(3inch, 1.5inch); for ( int y = 0; y <= 5; ++y ) { draw((0,y)--(18,y)); } draw((0,0)--(0,5)); draw((6,0)--(6,5)); draw((9,0)--(9,5)); draw((12,0)--(12,5)); draw((15,0)--(15,5)); draw((18,0)--(18,5)); draw(scale(0.8)*"50s", (7.5,4.5)); draw(scale(0.8)*"4", (7.5,3.5)); draw(scale(0.8)*"8", (7.5,2.5)); draw(scale(0.8)*"6", (7.5,1.5)); draw(scale(0.8)*"3", (7.5,0.5)); draw(scale(0.8)*"60s", (10.5,4.5)); draw(scale(0.8)*"7", (10.5,3.5)); draw(scale(0.8)*"4", (10.5,2.5)); draw(scale(0.8)*"4", (10.5,1.5)); draw(scale(0.8)*"9", (10.5,0.5)); draw(scale(0.8)*"70s", (13.5,4.5)); draw(scale(0.8)*"12", (13.5,3.5)); draw(scale(0.8)*"12", (13.5,2.5)); draw(scale(0.8)*"6", (13.5,1.5)); draw(scale(0.8)*"13", (13.5,0.5)); draw(scale(0.8)*"80s", (16.5,4.5)); draw(scale(0.8)*"8", (16.5,3.5)); draw(scale(0.8)*"15", (16.5,2.5)); draw(scale(0.8)*"10", (16.5,1.5)); draw(scale(0.8)*"9", (16.5,0.5)); label(scale(0.8)*"Country", (3,4.5)); label(scale(0.8)*"Brazil", (3,3.5)); label(scale(0.8)*"France", (3,2.5)); label(scale(0.8)*"Peru", (3,1.5)); label(scale(0.8)*"Spain", (3,0.5)); label(scale(0.9)*"Juan's Stamp Collection", (9,0), S); label(scale(0.9)*"Number of Stamps by Decade", (9,5), N);[/asy]


$\text{(A)}\ 3.5\text{ cents}\qquad\text{(B)}\ 4\text{ cents}\qquad\text{(C)}\ 4.5\text{ cents}\qquad\text{(D)}\ 5\text{ cents}\qquad\text{(E)}\ 5.5\text{ cents}$


Solution

$12*0.06*2=1.44$


$6*0.04=0.24$

$13*0.05=0.65$

Sum is $2.33$

Total there are $43$ stamps

$2.33/43=$ $\boxed{E}$

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