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

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==Problem 3==
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==Problem==
 
Carrie has a rectangular garden that measures <math>6</math> feet by <math>8</math> feet. She plants the entire garden with strawberry plants. Carrie is able to plant <math>4</math> strawberry plants per square foot, and she harvests an average of <math>10</math> strawberries per plant. How many strawberries can she expect to harvest?
 
Carrie has a rectangular garden that measures <math>6</math> feet by <math>8</math> feet. She plants the entire garden with strawberry plants. Carrie is able to plant <math>4</math> strawberry plants per square foot, and she harvests an average of <math>10</math> strawberries per plant. How many strawberries can she expect to harvest?
  
 
<math>\textbf{(A) }560 \qquad \textbf{(B) }960 \qquad \textbf{(C) }1120 \qquad \textbf{(D) }1920 \qquad \textbf{(E) }3840</math>
 
<math>\textbf{(A) }560 \qquad \textbf{(B) }960 \qquad \textbf{(C) }1120 \qquad \textbf{(D) }1920 \qquad \textbf{(E) }3840</math>
  
==Solution==
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==Solution 1==
The answer is the product of the area of the field, the amount of strawberries per plant, and the amount of plants in one square feet. The answer is <math>6 \times 8 \times 10 \times 4 = 1920</math> or <math>\boxed{\textbf{D }1920}</math>.
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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==
 
==Solution 2==
The area of the garden is <math>6 ft \times 8 ft = 48</math> square feet. Since Carrie plants <math>4</math> strawberry plants per square foot, it follows that she plants a total of <math>48 \times 4=192</math> strawberry plants. Since each strawberry plant produces on average 10 strawberries, it follows that she can expect to harvest <math>192 \times 10=1920</math> strawberries <math>\implies\boxed{\textbf{(D) }1920}</math>.<br>
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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>.
~jmansuri
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==Video Solution==
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https://youtu.be/eSxzI8P9_h8
  
 
==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 00:21, 10 January 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 $6 \cdot 8 \cdot 4 \cdot 10 = \boxed{\textbf{(D) }1920}$.

Video Solution

https://youtu.be/eSxzI8P9_h8

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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