Chads buys peanuts in 2 pound bags. How many 2 pound bags of peanut should chad buy so that he can fill the 5/6 pound bags without having any peanuts left over
6 bags uses 5 pounds
12 bags uses 10 pounds, or 5 large bags.
To solve this problem, we need to determine how many 2-pound bags of peanuts Chad should buy to fill the 5/6 pound bags without any leftovers.
Step 1: Convert 5/6 pounds to pounds.
- Since 1 pound is equal to 2/2 (or 12/12) pounds, we can convert 5/6 pounds to (5/6) * (12/12) = 60/72 pounds.
- Simplifying the fraction, we get 5/6 pounds = 5/6 * 60/72 = 50/72 pounds.
Step 2: Determine the number of 2-pound bags needed.
- Now, we need to figure out how many 2-pound bags are required to fill 50/72 pounds.
- Divide 50/72 by 2/2 (2 pounds) to get (50/72) / (2/2) = (50/72) * (2/2) = 100/144.
- Simplifying the fraction, we have 100/144 = 25/36 two-pound bags.
Therefore, Chad should buy 25/36 (or approximately 0.69) 2-pound bags of peanuts to fill the 5/6 pound bags without any leftovers. Since Chad cannot buy fractional bags, he should round up to the nearest whole number. Therefore, Chad will need to buy at least 1 bag of peanuts to fill the bags without any leftovers.
To solve this problem, we can set up a simple equation:
Let x be the number of 2 pound bags Chad needs to buy.
Each 2 pound bag can fill one 5/6 pound bag.
So, the equation is:
2 pounds/bag * x bags = 5/6 pounds/bag
To solve for x, we can multiply both sides of the equation by 6 to remove the fraction:
6 * (2 pounds/bag) * x bags = 6 * (5/6 pounds/bag)
12x = 5 pounds
Now, divide both sides of the equation by 12:
x = 5/12
Hence, Chad should buy 5/12 of a bag, or approximately 0.42 bags. However, since we can't buy a fraction of a bag, we need to round up to the nearest whole number.
Therefore, Chad should buy 1 bag of peanuts in order to fill the 5/6 pound bags without having any peanuts left over.