Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

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

(→‎Problem 9)
Line 1: Line 1:
 +
==Juan's Old Stamping Grounds==
  
−
== Problem 9 ==
+
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). In dollars and cents, how much did his South American stampes issued before the '70s cost him?
+
<center>
 +
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.)
 +
</center>
  
 +
<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>
  
−
<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>
+
==Problem==
 +
 
 +
His South American stamps issued before the '70s cost him
 +
 
 +
<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>
 +
 
 +
==Solution==
 +
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>.
 +
 
 +
==See Also==
 +
{{AMC8 box|year=2002|num-b=8|num-a=10}}

Revision as of 19:26, 23 December 2012

Juan's Old Stamping Grounds

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]

Problem

His South American stamps issued before the '70s cost him

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

Solution

The number of stamps from Brazil in the '50s and '60s is $4+7=11$, and they cost 6 cents each for a total of $11 \cdot \textdollar 0.06 = \textdollar 0.66$. The number of stamps from Peru in the '50s and '60s is $6+4=10$, and they cost 4 cents each for a total of $10 \cdot \textdollar 0.04 = \textdollar 0.40$. In total, he paid $0.66 + 0.40 = \boxed{\text{(B)}\ \textdollar 1.06}$.

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
Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2002_AMC_8_Problems/Problem_9&oldid=50148"