Difference between revisions of "2020 AMC 8 Problems/Problem 3"
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− | ==Problem | + | ==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== | + | ==Solution 1== |
− | + | Note that the unit of the answer is <b>strawberries</b>, which is the product of | |
− | + | * square feet | |
− | + | ||
− | + | * plants per square foot | |
− | + | * strawberries per plant | |
− | + | 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 | |
− | ==Video Solution== | + | ==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. | ||
+ | |||
+ | ==Video Solution by WhyMath== | ||
https://youtu.be/7S0wAZMy2ZQ | https://youtu.be/7S0wAZMy2ZQ | ||
~savannahsolver | ~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 | ||
==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}} |
Latest revision as of 23:32, 11 January 2022
Contents
Problem
Carrie has a rectangular garden that measures feet by feet. She plants the entire garden with strawberry plants. Carrie is able to plant strawberry plants per square foot, and she harvests an average of strawberries per plant. How many strawberries can she expect to harvest?
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
~MRENTHUSIASM ~Bobthegod78
Solution 2
The area of the garden is square feet. Since Carrie plants strawberry plants per square foot, there are a total of strawberry plants, each of which produces strawberries on average. Accordingly, she can expect to harvest strawberries.
Video Solution by WhyMath
~savannahsolver
Video Solution by The Learning Royal
~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
See also
2020 AMC 8 (Problems • Answer Key • Resources) | ||
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.