math
posted by Chris .
Chad buys peanuts in 2 pound bags. He repackages them into bags that hold 5/6 pound of peanuts. How many 2 pound bags of peanuts should Chad buy so that he can fill the 5/6 pound bags without having any peanuts left over?

let the number of bags needed be n
so 2n ÷ (5/6) must be a whole number
= 2n(6/5)
= 12n/5
The smallest value of n is 5
So he should buy 5 of the 2 lbs bags
Check:
if n=5 , he will have 10 lbs.
number of smaller bags he can fill
= 10 ÷ (5/6)
= 10(6/5)
= 12 > exact number of bags, no peanuts left over. 
3 bags
in 3 bags he will have 6 pounds. If for each bag he needs 5/6 of a pound this means he will have 1/6 x 6 leftover, which is exactly another bag.
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