& \mathbf{Describe} && \text{There are two pan balances,} \ \text{C} \ \text{and} \ \text{D}.\!\\ &&& \text{C}: \text{The pans are not level.}\!\\&&& \text{D}: \text{The pans are level.}\!\\ &&& \text{There are two different boxes,} \ p \ \text{and} \ n. \ \text{There is an} \ 8 \ \text{pound box on} \ \text{D}.\\& \mathbf{My \ Job} && \text{Figure out the weights of} \ p \ \text{and} \ n. \ \text{Decide if other weights are possible}.\!\\& \mathbf{Plan} && \text{C}: \ 2 \ p \ \text{weighs less than} \ n.\!\\&&& \text{D}: \text{The pan with} \ n \ \text{weighs the same as} \ 8 \ \text{pounds}.\!\\&&& \qquad \text{Start with this fact}.\!\\& \mathbf{Solve} && \text{C}: \ 2p < 8 \ \text{pounds so} \ p = 1, 2 \ \text{or} \ 3 \ \text{pounds}\!\\&&& \text{D}: \  n = 8\\& \mathbf{Check} && \text{C}: \ 1+1 <8; 2+2<8; 3+3<8
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