If 10 jugs of H2o fill 5/8 of a bucket. Another 4 jugs and 5 cups of H2o are needed to fill the remaining parts of buckets. How many cups of H2o can fill a bucket?
10 jugs fill 5/8 buckets, so
1 jug fills 5/80 = 1/16 bucket, so
1 bucket fills 16 jugs
3/8 bucket remains unfilled, so that's 3/8 * 16 = 6 jugs
6 jugs = 4 jugs + 5 cups, so
2 jugs = 5 cups
1 jug = 5/2 cups
a bucket = 16 jugs = 16*5/2 = 40 cups
40
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To solve this problem, we'll need to follow these steps:
1. Determine the amount of water that 10 jugs fill in the bucket.
2. Calculate the amount of the bucket that remains unfilled.
3. Convert the amount needed (4 jugs and 5 cups) to cups.
4. Add the remaining amount to the initial amount filled by the 10 jugs.
5. Calculate the total amount of water that can fill a bucket in cups.
Step 1: Determine the amount of water that 10 jugs fill in the bucket.
We know that 10 jugs fill 5/8 of a bucket. To find out how much water 1 jug fills, we divide 5/8 by 10:
(5/8) รท 10 = 5/80
Step 2: Calculate the amount of the bucket that remains unfilled.
To determine how much of the bucket remains unfilled, we subtract the amount filled by 10 jugs from the total capacity of the bucket, which is 8/8 or 1 whole:
1 - 5/8 = 8/8 - 5/8 = 3/8
Step 3: Convert the amount needed (4 jugs and 5 cups) to cups.
We need to convert 4 jugs and 5 cups into cups. Since 1 jug is already expressed as 5/80 of a bucket, we can calculate the amount needed in cups:
4 jugs + 5 cups = (4 x 5/80) + 5
= 20/80 + 5
= 20/80 + 400/80
= 420/80
= 21/4
Step 4: Add the remaining amount to the initial amount filled by the 10 jugs.
To find out the total amount of water needed to fill the bucket, we add the remaining amount (3/8) to the amount needed (21/4):
3/8 + 21/4 = (3 x 1/8) + 21/4
= 3/8 + 21/4
= 3/8 + 42/8
= 45/8
Step 5: Calculate the total amount of water that can fill a bucket in cups.
Finally, we need to convert the answer from Step 4, which is represented as 45/8, into cups:
45/8 x 5 = (45 x 5)/8
= 225/8
= 28 1/8
Therefore, 28 1/8 cups of water can fill a bucket.