SOLUTION: Nana had enough batter to make eight 10" diameter pancakes. She had 32 grandchildren to feed that morning so she decided to use algebra to find out what diameter pancakes she shoul

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Question 715688: Nana had enough batter to make eight 10" diameter pancakes. She had 32 grandchildren to feed that morning so she decided to use algebra to find out what diameter pancakes she should pour to allow each one of her grandchildren to have a pancake. What diameter pancakes should Nana make?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
We can assume the spread area of the entire batter batch will be the same no matter how many of what sized pancakes are made from the entire batch.

The known 8 each of 10 inch diameter pancakes will cover that described area of 8%2Api%2A%2810%2F2%29%5E2 square inches. The radius there is 10 diameter inches divided by 2.

Now, we want to divide that batch's area into 32 and we want the circles to have some other diameter. We must use 32 of these circles, and the area must be the same as 8%2Api%2A%2810%2F2%29%5E2 square inches. We use d as a variable for the unknown diameter.

highlight%288%2Api%2A%2810%2F2%29%5E2=32%2Api%2A%28d%2F2%29%5E2%29
%288%2Api%2A5%5E2%29%2F%2832%2Api%29=%281%2F4%29d%5E2
d%5E2=25
The answer: d=5

Nana will make 32 each of 5 inch diameter pancakes.