Difference between revisions of "2018 AMC 10B Problems/Problem 1"

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Kate bakes 20-inch by 18-inch pan of cornbread. The cornbread is cut into pieces that measure 2 inches by 2 inches. How many pieces of cornbread does the pan contain?
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==Problem==
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Kate bakes a <math>20</math>-inch by <math>18</math>-inch pan of cornbread. The cornbread is cut into pieces that measure <math>2</math> inches by <math>2</math> inches. How many pieces of cornbread does the pan contain?
  
 
<math>\textbf{(A) } 90 \qquad \textbf{(B) } 100 \qquad \textbf{(C) } 180 \qquad \textbf{(D) } 200 \qquad \textbf{(E) } 360</math>
 
<math>\textbf{(A) } 90 \qquad \textbf{(B) } 100 \qquad \textbf{(C) } 180 \qquad \textbf{(D) } 200 \qquad \textbf{(E) } 360</math>
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== Solution 1 ==
 
== Solution 1 ==
  
The area of the pan is <math>20\cdot18</math> = <math>360</math>. Since the area of each piece is <math>4</math>, there are <math>360</math>/<math>40</math> = <math>90</math> pieces. Thus, the answer is A.
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The area of the pan is <math>20\cdot18</math> = <math>360</math>. Since the area of each piece is <math>4</math>, there are <math>\frac{360}{4} = 90</math> pieces. Thus, the answer is <math>\boxed{A}</math>.
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== Solution 2 ==
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By dividing each of the dimensions by <math>2</math>, we get a <math>10\times9</math> grid which makes <math>90</math> pieces. Thus, the answer is <math>\boxed{A}</math>.
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==Video Solution==
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https://youtu.be/o5MUHOmF1zo
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~savannahsolver
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==See Also==
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{{AMC10 box|year=2018|ab=B|before=First Problem|num-a=2}}
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{{AMC12 box|year=2018|ab=B|before=First Problem|num-a=2}}
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{{MAA Notice}}

Latest revision as of 16:50, 16 June 2020

Problem

Kate bakes a $20$-inch by $18$-inch pan of cornbread. The cornbread is cut into pieces that measure $2$ inches by $2$ inches. How many pieces of cornbread does the pan contain?

$\textbf{(A) } 90 \qquad \textbf{(B) } 100 \qquad \textbf{(C) } 180 \qquad \textbf{(D) } 200 \qquad \textbf{(E) } 360$

Solution 1

The area of the pan is $20\cdot18$ = $360$. Since the area of each piece is $4$, there are $\frac{360}{4} = 90$ pieces. Thus, the answer is $\boxed{A}$.

Solution 2

By dividing each of the dimensions by $2$, we get a $10\times9$ grid which makes $90$ pieces. Thus, the answer is $\boxed{A}$.

Video Solution

https://youtu.be/o5MUHOmF1zo

~savannahsolver

See Also

2018 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 2
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 AMC 10 Problems and Solutions
2018 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 2
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 AMC 12 Problems and Solutions

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