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==Problem==
A grocer stacks oranges in a pyramid-like stack whose rectangular base is 5 oranges by 8 oranges.  Each orange above the first level rests in a pocket formed by four oranges below.  The stack is completed by a single row of oranges.  How many oranges are in the stack?

<math> \mathrm{(A) \ } 96 \qquad \mathrm{(B) \ } 98 \qquad \mathrm{(C) \ } 100 \qquad \mathrm{(D) \ } 101 \qquad \mathrm{(E) \ } 134  </math>

==Solution==
There are <math>5\times8=40</math> oranges on the 1st layer of the stack.  When the 2nd layer is added on top of the first, it will be a layer of <math>4\times7=28</math> oranges.  When the third layer is added on top of the 2nd, it will be a layer of <math>3\times6=18</math> oranges, etc.

Therefore, there are <math>5\times8+4\times7+3\times6+2\times5+1\times4=40+28+18+10+4=100</math> oranges in the stack <math>\Rightarrow\mathrm{(C)}</math>.

== See also ==
{{AMC10 box|year=2004|ab=A|num-b=6|num-a=8}}

[[Category:Introductory Algebra Problems]]