2018 AMC 10B Problems/Problem 1: Difference between revisions

Revision as of 14:34, 23 December 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

2018 AMC 10B (Problems • Answer Key • Resources)
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2018 AMC 12B (Problems • Answer Key • Resources)
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All AMC 12 Problems and Solutions

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: File missing

@@ Line 1: / Line 1: @@
-Problem:
+==Problem==
-Suppose we write down the smallest (positive) <math>2</math>-digit, <math>3</math>-digit, and <math>4</math>-digit multiples of <math>8</math>.
+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?
-Problem:
+<math>\textbf{(A) } 90 \qquad \textbf{(B) } 100 \qquad \textbf{(C) } 180 \qquad \textbf{(D) } 200 \qquad \textbf{(E) } 360</math>
-Suppose we write down the smallest (positive) <math>2</math>-digit, <math>3</math>-digit, and <math>4</math>-digit multiples of <math>8</math>.
-What is the sum of these three numbers?
+== 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>\frac{360}{4} = 90</math> pieces. Thus, the answer is <math>\boxed{A}</math>.
 == Solution 2 ==

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