2002 AMC 8 Problems/Problem 10: Difference between revisions
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The price of all the stamps in the '70s together over the total number of stamps is equal to the average price. | The price of all the stamps in the '70s together over the total number of stamps is equal to the average price. | ||
<cmath>\frac{(12)(0.06)+(12)(0.06)+(6)(0.04)+(13)(0.05)}{12+12+6+13} | <cmath> | ||
= \frac{0.72+0.72+0.24+0.65}{43}\\ | \begin{align*} | ||
= \frac{2.33}{43} \approx \boxed{\text{(E)}\ 5.5\ \text{cents}}</cmath> | \frac{(12)(0.06)+(12)(0.06)+(6)(0.04)+(13)(0.05)}{12+12+6+13} | ||
&= \frac{0.72+0.72+0.24+0.65}{43} \\ | |||
&= \frac{2.33}{43} \\ | |||
&\approx \boxed{\text{(E)}\ 5.5\ \text{cents}} | |||
\end{align*} | |||
</cmath> | |||
==Video Solution by WhyMath== | ==Video Solution by WhyMath== | ||
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{{AMC8 box|year=2002|num-b=9|num-a=11}} | {{AMC8 box|year=2002|num-b=9|num-a=11}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
[[Category:Introductory Algebra Problems]] | |||
Latest revision as of 16:50, 25 June 2025
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 <= 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]](http://latex.artofproblemsolving.com/f/6/7/f679bb00d960506089f9cd632a80bd218347de4e.png)
The average price of his '70s stamps is closest to
Solution
The price of all the stamps in the '70s together over the total number of stamps is equal to the average price.
Video Solution by WhyMath
See Also
| 2002 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: File missing
