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Difference between revisions of "2002 AMC 8 Problems/Problem 9"

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==Juan's Old Stamping Grounds==
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==Problem==
  
 
Problems 8,9 and 10 use the data found in the accompanying paragraph and table:
 
Problems 8,9 and 10 use the data found in the accompanying paragraph and table:
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label(scale(0.9)*"Number of Stamps by Decade", (9,5), N);</asy>
 
label(scale(0.9)*"Number of Stamps by Decade", (9,5), N);</asy>
  
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==Problem==
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In dollars and cents, how much did his South American stamps issued before the ’70s cost him?
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How many of his European stamps were issued in the <math>80\text{'s}?</math>
 
  
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<math>\text{(A)}\ \textdollar 0.40 \qquad \text{(B)}\ \textdollar 1.06 \qquad \text{(C)}\ \textdollar 1.80 \qquad \text{(D)}\ \textdollar 2.38 \qquad \text{(E)}\ \textdollar 2.64</math>
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<math>\text{(A)}\ \$0.40 \qquad \text{(B)}\ \$1.06 \qquad \text{(C)}\ \$1.80 \qquad \text{(D)}\ \$2.38 \qquad \text{(E)}\ \$2.64</math>
  
 
==Solution==
 
==Solution==
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The number of stamps from Brazil in the '50s and '60s is <math>4+7=11</math>, and they cost 6 cents each for a total of <math>11 \cdot \textdollar 0.06 = \textdollar 0.66</math>. The number of stamps from Peru in the '50s and '60s is <math>6+4=10</math>, and they cost 4 cents each for a total of <math>10 \cdot \textdollar 0.04 = \textdollar 0.40</math>. In total, he paid <math>0.66 + 0.40 = \boxed{\text{(B)}\ \textdollar 1.06}</math>.
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Brazil 50s and 60s total 11 stamps with each 6 cents, Peru 50s and 60s total 10 stamps with each 4 cents. So total <math>11*0.06+10*0.04 = \boxed{\text{(B)}\ \$1.06}</math>  
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==Video Solution by WhyMath==
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https://youtu.be/RWqatORHMow
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2002|num-b=8|num-a=10}}
 
{{AMC8 box|year=2002|num-b=8|num-a=10}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 13:29, 29 October 2024

Problem

Problems 8,9 and 10 use the data found in the accompanying paragraph and table:

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.)

[asy] /* AMC8 2002 #8, 9, 10 Problem */ size(3inch, 1.5inch); for ( int y = 0; y &lt;= 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]

In dollars and cents, how much did his South American stamps issued before the ’70s cost him?

$\text{(A)}\ $0.40 \qquad \text{(B)}\ $1.06 \qquad \text{(C)}\ $1.80 \qquad \text{(D)}\ $2.38 \qquad \text{(E)}\ $2.64$

Solution

Brazil 50s and 60s total 11 stamps with each 6 cents, Peru 50s and 60s total 10 stamps with each 4 cents. So total $11*0.06+10*0.04 = \boxed{\text{(B)}\ $1.06}$

Video Solution by WhyMath

https://youtu.be/RWqatORHMow

See Also

2002 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 8 		Followed by
Problem 10
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 AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

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