Difference between revisions of "2020 AMC 8 Problems/Problem 14"
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~Pi_Pup | ~Pi_Pup | ||
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+ | ==Solution 3== | ||
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+ | After reading the question, we notice that the dashed line is the average population of each city. Also, that dashed line is slightly less than <math>5\,000</math>. Since there are <math>20</math> cities, the answer is slightly less than <math>20\cdot 5\,000\approx 100\,000</math> which is closest to <math>\textbf{(D) }95{,}000</math>. | ||
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+ | -franzliszt | ||
==See also== | ==See also== | ||
{{AMC8 box|year=2020|num-b=13|num-a=15}} | {{AMC8 box|year=2020|num-b=13|num-a=15}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 14:58, 18 November 2020
There are cities in the County of Newton. Their populations are shown in the bar chart below. The average population of all the cities is indicated by the horizontal dashed line. Which of the following is closest to the total population of all
cities?
Diagram by sircalcsalot
Contents
Solution 1
The average is given to be . This is because the dotted line is halfway in between
and
. There are
cities, so our answer is simply
Solution 2
We know that the average () of these group of numbers is the sum (
) divided by
, so we can make the equation
. Since the average is
, we can solve for
to get
~Pi_Pup
Solution 3
After reading the question, we notice that the dashed line is the average population of each city. Also, that dashed line is slightly less than . Since there are
cities, the answer is slightly less than
which is closest to
.
-franzliszt
See also
2020 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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 |
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