SOLUTION: A school has a telephone system for letting families know about emergency school closings. The system is a pyramid with 5 layers. Three parents are on the top layer of the pyramid.

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Question 497868: A school has a telephone system for letting families know about emergency school closings. The system is a pyramid with 5 layers. Three parents are on the top layer of the pyramid. Each parent in each layer calls three different parents. How many parents are in the chain?
Answer by Flannery(124) About Me  (Show Source):
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LAYER ONE: 3
THREE PARENTS CALL THREE PARENTS EACH GIVING
LAYER TWO: 3*3=9 (3^2) THE NUMBER OF CALLS MADE EQUALS PARENTS IN THIS LAYER
NINE PARENTS CALL THREE PARENTS EACH GIVING
LAYER THREE: 3*3*3=27 (3^3) NINE PARENTS TIMES THREE CALLS EQUALS PARENTS IN THIS LAYER
TWENTY SEVEN PARENTS CALL THREE PARENTS EACH GIVING
LAYER FOUR: 3*3*3*3=81 (3^4) TWENTY SEVEN PARENTS TIMES THREE CALLS EQUALS THE NUMBER OF PARENTS IN THIS LAYER
EIGHTY ONE PARENTS CALL THREE PARENTS EACH GIVING
LAYER FIVE: 3*3*3*3*3=243 (3^5) EIGHTY ONE PARENTS TIMES THREE CALLS EQUALS THE NUMBER OF PARENTS IN THIS LAYER
ADD THE STACK OF LAYERS TOGETHER
3+3^2+3^3+3^4+3^5=
3+9+27+81+243=363