Difference between revisions of "2020 AMC 8 Problems/Problem 14"
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==Solution 1== | ==Solution 1== | ||
− | We can see that the dotted line is halfway between <math>4{,}500</math> and <math>5{,}000</math>, so is at <math>4{,}750</math>. As this is the average population of all <math>20</math> cities, the total population is simply <math>4{,}750 \cdot 20 = \boxed{\textbf{(D) }95{,}000}</math>. | + | We can see that the dotted line is exactly halfway between <math>4{,}500</math> and <math>5{,}000</math>, so it is at <math>4{,}750</math>. As this is the average population of all <math>20</math> cities, the total population is simply <math>4{,}750 \cdot 20 = \boxed{\textbf{(D) }95{,}000}</math>. |
==Solution 2 (estimation)== | ==Solution 2 (estimation)== | ||
− | The dashed line, which represents the average population of each city, is slightly below <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> | + | The dashed line, which represents the average population of each city, is slightly below <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>\boxed{\textbf{(D) }95{,}000}</math>. |
==Video Solution== | ==Video Solution== | ||
− | https://youtu.be/ | + | https://youtu.be/xjwDsaRE_Wo |
==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}} |
Latest revision as of 18:47, 6 January 2021
Problem
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?
Solution 1
We can see that the dotted line is exactly halfway between and , so it is at . As this is the average population of all cities, the total population is simply .
Solution 2 (estimation)
The dashed line, which represents the average population of each city, is slightly below . Since there are cities, the answer is slightly less than , which is closest to .
Video Solution
See also
2020 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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All AJHSME/AMC 8 Problems and Solutions |
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