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

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We have <cmath>\left(6 \ \cancel{\mathrm{ft}}\cdot8 \ \cancel{\mathrm{ft}}\right)\cdot\left(4 \ \frac{\bcancel{\mathrm{plants}}}{\cancel{\mathrm{ft}^2}}\right)\cdot\left(10 \ \frac{\mathrm{strawberries}}{\bcancel{\mathrm{plant}}}\right)=6\cdot8\cdot4\cdot10 \ \mathrm{strawberries}=\boxed{\textbf{(D) }1920} \ \mathrm{strawberries}.</cmath>
 
We have <cmath>\left(6 \ \cancel{\mathrm{ft}}\cdot8 \ \cancel{\mathrm{ft}}\right)\cdot\left(4 \ \frac{\bcancel{\mathrm{plants}}}{\cancel{\mathrm{ft}^2}}\right)\cdot\left(10 \ \frac{\mathrm{strawberries}}{\bcancel{\mathrm{plant}}}\right)=6\cdot8\cdot4\cdot10 \ \mathrm{strawberries}=\boxed{\textbf{(D) }1920} \ \mathrm{strawberries}.</cmath>
 
~MRENTHUSIASM
 
~MRENTHUSIASM
 +
 +
==Video Solution by North America Math Contest Go Go Go==
 +
https://www.youtube.com/watch?v=_IjQnXnVKeU
 +
(Please subscribe I Really need them!)
  
 
==Video Solution by WhyMath==
 
==Video Solution by WhyMath==

Revision as of 01:04, 19 June 2021

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

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.

Solution 2

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 $6 \cdot 8 \cdot 4 \cdot 10 = \boxed{\textbf{(D) }1920}$.

Solution 3 (One Sentence)

We have \[\left(6 \ \cancel{\mathrm{ft}}\cdot8 \ \cancel{\mathrm{ft}}\right)\cdot\left(4 \ \frac{\bcancel{\mathrm{plants}}}{\cancel{\mathrm{ft}^2}}\right)\cdot\left(10 \ \frac{\mathrm{strawberries}}{\bcancel{\mathrm{plant}}}\right)=6\cdot8\cdot4\cdot10 \ \mathrm{strawberries}=\boxed{\textbf{(D) }1920} \ \mathrm{strawberries}.\] ~MRENTHUSIASM

Video Solution by North America Math Contest Go Go Go

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

Video Solution by WhyMath

https://youtu.be/7S0wAZMy2ZQ

~savannahsolver

Video Solution

https://youtu.be/eSxzI8P9_h8

Video Solution by Interstigation

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

~Interstigation

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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