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arranging toothpicks


Toothpicks are used to build a rectangular grid that is 20 toothpicks long and 10 toothpicks wide. The grid is filled with squares that have 1 toothpick on each side. What is the total number of toothpicks used?
If a represents the number of toothpicks in the length of a grid and b represents the number of toothpicks in the width of a grid (again, the grid is filled with squares that have 1 toothpick on each side), write an expression representing the total number of toothpicks in any rectangular grid of this sort.



(Source: Mathematics Teaching in the Middle School, May 1996)



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