Difference between revisions of "2013 AMC 8 Problems/Problem 22"

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==Problem==
 
==Problem==
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Toothpicks are used to make a grid that is 60 toothpicks long and 32 toothpicks wide. How many toothpicks are used altogether?
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[asy]
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picture corner;
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draw(corner,(5,0)--(35,0));
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draw(corner,(0,-5)--(0,-35));
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for (int i=0; i<3; ++i)
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{
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for (int j=0; j>-2; --j)
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{
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if ((i-j)<3)
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{
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add(corner,(50i,50j));
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}
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}
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}
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draw((5,-100)--(45,-100));
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draw((155,0)--(185,0),dotted+linewidth(2));
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draw((105,-50)--(135,-50),dotted+linewidth(2));
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draw((100,-55)--(100,-85),dotted+linewidth(2));
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draw((55,-100)--(85,-100),dotted+linewidth(2));
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draw((50,-105)--(50,-135),dotted+linewidth(2));
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draw((0,-105)--(0,-135),dotted+linewidth(2));[/asy]
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<math>\textbf{(A)}\ 1920 \qquad \textbf{(B)}\ 1952 \qquad \textbf{(C)}\ 1980 \qquad \textbf{(D)}\ 2013 \qquad \textbf{(E)}\ 3952</math>
  
 
==Solution==
 
==Solution==

Revision as of 12:53, 27 November 2013

Problem

Toothpicks are used to make a grid that is 60 toothpicks long and 32 toothpicks wide. How many toothpicks are used altogether?

[asy] picture corner; draw(corner,(5,0)--(35,0)); draw(corner,(0,-5)--(0,-35)); for (int i=0; i<3; ++i) { for (int j=0; j>-2; --j) { if ((i-j)<3) { add(corner,(50i,50j)); } } } draw((5,-100)--(45,-100)); draw((155,0)--(185,0),dotted+linewidth(2)); draw((105,-50)--(135,-50),dotted+linewidth(2)); draw((100,-55)--(100,-85),dotted+linewidth(2)); draw((55,-100)--(85,-100),dotted+linewidth(2)); draw((50,-105)--(50,-135),dotted+linewidth(2)); draw((0,-105)--(0,-135),dotted+linewidth(2));[/asy]

$\textbf{(A)}\ 1920 \qquad \textbf{(B)}\ 1952 \qquad \textbf{(C)}\ 1980 \qquad \textbf{(D)}\ 2013 \qquad \textbf{(E)}\ 3952$

Solution

See Also

2013 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 21
Followed by
Problem 23
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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