Difference between revisions of "2020 AMC 8 Problems/Problem 3"

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==Solution 1==
 
==Solution 1==
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Note that the unit of the answer is <b>strawberries</b>, which is the product of
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* square feet
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* plants per square foot
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* strawberries per plant
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By conversion factors, we have <cmath>\left(6 \ \color{red}\cancel{\mathrm{ft}}\color{black}\cdot8 \ \color{red}\cancel{\mathrm{ft}}\color{black}\right)\cdot\left(4 \ \frac{\color{green}\cancel{\mathrm{plants}}}{\color{red}\cancel{\mathrm{ft}^2}}\right)\cdot\left(10 \ \frac{\mathrm{strawberries}}{\color{green}\cancel{\mathrm{plant}}}\right)=6\cdot8\cdot4\cdot10 \ \mathrm{strawberries}=\boxed{\textbf{(D) }1920} \ \mathrm{strawberries}.</cmath>
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~MRENTHUSIASM ~Bobthegod78
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==Solution 2==
 
The area of the garden is <math>6 \cdot 8 = 48</math> square feet. Since Carrie plants <math>4</math> strawberry plants per square foot, there are a total of <math>48 \cdot 4=192</math> strawberry plants, each of which produces <math>10</math> strawberries on average. Accordingly, she can expect to harvest <math>192 \cdot 10 = \boxed{\textbf{(D) }1920}</math> strawberries.
 
The area of the garden is <math>6 \cdot 8 = 48</math> square feet. Since Carrie plants <math>4</math> strawberry plants per square foot, there are a total of <math>48 \cdot 4=192</math> strawberry plants, each of which produces <math>10</math> strawberries on average. Accordingly, she can expect to harvest <math>192 \cdot 10 = \boxed{\textbf{(D) }1920}</math> strawberries.
  
==Solution 2==
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==Video Solution by WhyMath==
Looking at the units of each quantity, we observe that the answer will be the product of the number of square feet, the number of plants per square foot, and the number of strawberries per plant. This gives <math>6 \cdot 8 \cdot 4 \cdot 10 = \boxed{\textbf{(D) }1920}</math>.
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https://youtu.be/7S0wAZMy2ZQ
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~savannahsolver
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==Video Solution by The Learning Royal==
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https://youtu.be/eSxzI8P9_h8
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~The Learning Royal
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==Video Solution by Interstigation==
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https://youtu.be/YnwkBZTv5Fw?t=92
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~Interstigation
  
==Video Solution==
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==Video Solution by North America Math Contest Go Go Go==
https://youtu.be/SPNobOd4t1c
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https://www.youtube.com/watch?v=_IjQnXnVKeU
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(Please subscribe I Really need them!)
  
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~North America Math Contest Go Go Go
  
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==Video Solution by STEMbreezy==
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https://youtu.be/L_vDc-i585o?list=PLFcinOE4FNL0TkI-_yKVEYyA_QCS9mBNS&t=89
  
https://youtu.be/eSxzI8P9_h8
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~STEMbreezy
  
 
==See also==  
 
==See also==  
 
{{AMC8 box|year=2020|num-b=2|num-a=4}}
 
{{AMC8 box|year=2020|num-b=2|num-a=4}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 22:52, 24 December 2022

Problem

Carrie has a rectangular garden that measures $6$ feet by $8$ feet. She plants the entire garden with strawberry plants. Carrie is able to plant $4$ strawberry plants per square foot, and she harvests an average of $10$ strawberries per plant. How many strawberries can she expect to harvest?

$\textbf{(A) }560 \qquad \textbf{(B) }960 \qquad \textbf{(C) }1120 \qquad \textbf{(D) }1920 \qquad \textbf{(E) }3840$

Solution 1

Note that the unit of the answer is strawberries, which is the product of

  • square feet
  • plants per square foot
  • strawberries per plant

By conversion factors, we have \[\left(6 \ \color{red}\cancel{\mathrm{ft}}\color{black}\cdot8 \ \color{red}\cancel{\mathrm{ft}}\color{black}\right)\cdot\left(4 \ \frac{\color{green}\cancel{\mathrm{plants}}}{\color{red}\cancel{\mathrm{ft}^2}}\right)\cdot\left(10 \ \frac{\mathrm{strawberries}}{\color{green}\cancel{\mathrm{plant}}}\right)=6\cdot8\cdot4\cdot10 \ \mathrm{strawberries}=\boxed{\textbf{(D) }1920} \ \mathrm{strawberries}.\]

~MRENTHUSIASM ~Bobthegod78

Solution 2

The area of the garden is $6 \cdot 8 = 48$ square feet. Since Carrie plants $4$ strawberry plants per square foot, there are a total of $48 \cdot 4=192$ strawberry plants, each of which produces $10$ strawberries on average. Accordingly, she can expect to harvest $192 \cdot 10 = \boxed{\textbf{(D) }1920}$ strawberries.

Video Solution by WhyMath

https://youtu.be/7S0wAZMy2ZQ

~savannahsolver

Video Solution by The Learning Royal

https://youtu.be/eSxzI8P9_h8

~The Learning Royal

Video Solution by Interstigation

https://youtu.be/YnwkBZTv5Fw?t=92

~Interstigation

Video Solution by North America Math Contest Go Go Go

https://www.youtube.com/watch?v=_IjQnXnVKeU (Please subscribe I Really need them!)

~North America Math Contest Go Go Go

Video Solution by STEMbreezy

https://youtu.be/L_vDc-i585o?list=PLFcinOE4FNL0TkI-_yKVEYyA_QCS9mBNS&t=89

~STEMbreezy

See also

2020 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 2
Followed by
Problem 4
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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