Chad buys peanuts in 2-pound bags. He repackages the into bags the 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?
2 is 12/6
so you need the lowest common multiple of 12 and 5 ... 60
60/6 = 10
... five 2 lb bags
or
number of bags needed --- n
amount of peanuts he bought 2n lbs
number of bags he needs to buy
= 2n/(5/6)
= 12n/5 <---- must be a whole number
the smallest number of n to make it so, is n = 5
number of bags needed = 5
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To find out how many 2-pound bags of peanuts Chad should buy, we need to determine the number of 2-pound bags that can fit evenly into bags that hold 5/6 pound of peanuts without any leftovers.
First, let's convert the 5/6-pound bag to an equivalent fraction of 2 pounds:
5/6 pound = (5/6) * 2 = 10/6 pounds = 5/3 pounds
Now we know that each bag Chad repackages should hold 5/3 pounds of peanuts, which is equivalent to 2/3 of a 2-pound bag.
To find out how many 2-pound bags Chad needs, we can divide the weight of a 5/3-pound bag by the weight of a 2-pound bag:
(5/3 pounds) / (2 pounds/bag) = (5/3) / (2/1) = 5/3 * 1/2 = 5/6
So, Chad needs to buy 5/6 of a 2-pound bag for each bag he repackages.
However, since we can't buy partial bags, Chad should round up the result to the nearest whole number. Therefore, Chad should buy 1 whole bag for each 5/6-pound bag.
Hence, Chad should buy 1 2-pound bag of peanuts for each bag that holds 5/6 pound of peanuts, in order to have enough without any peanuts left over.