Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2011 AMC 8 Problems/Problem 2"

m (Solution Heading)
 
(5 intermediate revisions by 5 users not shown)
Line 2: Line 2:
 
Karl's rectangular vegetable garden is <math> 20 </math> feet by <math> 45 </math> feet, and Makenna's is <math> 25 </math> feet by <math> 40 </math> feet. Whose garden is larger in area?
 
Karl's rectangular vegetable garden is <math> 20 </math> feet by <math> 45 </math> feet, and Makenna's is <math> 25 </math> feet by <math> 40 </math> feet. Whose garden is larger in area?
  
−
<math>\text{(A) Karl's garden is larger by 100 square feet.}</math>
+
<math>\textbf{(A)}\ \text{Karl's garden is larger by 100 square feet.}</math>
  
−
<math>\text{(B) Karl's garden is larger by 25 square feet.}</math>
+
<math>\textbf{(B)}\ \text{Karl's garden is larger by 25 square feet.}</math>
 
   
 
   
−
<math>\text{(C) The gardens are the same size.}</math>  
+
<math>\textbf{(C)}\ \text{The gardens are the same size.}</math>  
  
−
<math>\text{(D) Makenna's garden is larger by 25 square feet.}</math>
+
<math>\textbf{(D)}\ \text{Makenna's garden is larger by 25 square feet.}</math>
  
−
<math>\text{(E) Makenna's garden is larger by 100 square feet.}</math>
+
<math>\textbf{(E)}\ \text{Makenna's garden is larger by 100 square feet.}</math>
  
 
==Solution==
 
==Solution==
 +
 +
The area of a rectangle is given by the formula length times width. Karl's garden is <math>20 \times 45 = 900</math> square feet and Makenna's garden is <math>25 \times 40 = 1000</math> square feet. Since <math>1000 > 900,</math> Makenna's garden is larger by <math>1000-900=100</math> square feet. <math>\Rightarrow \boxed{ \textbf{(E)}\ \text{Makenna's garden is larger by 100 square feet.} }</math>
 +
 +
==Video Solution by WhyMath==
 +
https://youtu.be/CzAPGrFs0xs
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2011|num-b=1|num-a=3}}
 
{{AMC8 box|year=2011|num-b=1|num-a=3}}
 +
{{MAA Notice}}

Latest revision as of 10:01, 18 November 2024

Problem

Karl's rectangular vegetable garden is $20$ feet by $45$ feet, and Makenna's is $25$ feet by $40$ feet. Whose garden is larger in area?

$\textbf{(A)}\ \text{Karl's garden is larger by 100 square feet.}$

$\textbf{(B)}\ \text{Karl's garden is larger by 25 square feet.}$

$\textbf{(C)}\ \text{The gardens are the same size.}$

$\textbf{(D)}\ \text{Makenna's garden is larger by 25 square feet.}$

$\textbf{(E)}\ \text{Makenna's garden is larger by 100 square feet.}$

Solution

The area of a rectangle is given by the formula length times width. Karl's garden is $20 \times 45 = 900$ square feet and Makenna's garden is $25 \times 40 = 1000$ square feet. Since $1000 > 900,$ Makenna's garden is larger by $1000-900=100$ square feet. $\Rightarrow \boxed{ \textbf{(E)}\ \text{Makenna's garden is larger by 100 square feet.} }$

Video Solution by WhyMath

https://youtu.be/CzAPGrFs0xs

See Also

2011 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 1 		Followed by
Problem 3
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. AMC logo.png

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2011_AMC_8_Problems/Problem_2&oldid=234876"