There are two unmarked buckets by a stream. The buckets hold 19 and 8 gallons of water, respectively. How can 14 gallons of water be obtained, to take home? Complete the sequence below. The numbers represent the number of gallons in each bucket in each successive step.

9514 1404 393

  Fill the 19-gal bucket. Use that to fill the 8-gal bucket twice, so that 3 gal remains in the 19-gal bucket. Move that to the 8-gal bucket. Fill the 19-gal bucket again and use that to top off the 8-gal bucket. The 19-gal bucket now contains 14 gallons.

Step-by-step explanation:

The problem is equivalent to solving ...

  19a +8b = 14

One solution is (a, b) = (2, -3). That means you can obtain the required amount by filling the 19-gallon bucket 2 times, and using that source to fill (and empty) the 8-gallon bucket 3 times.

The third attempt to fill the 8-gallon bucket from the 19-gallon bucket will result in only 3 gallons in the 8-gallon bucket. The last 5 gallons needed to finish filling the 8-gallon bucket the third time come from the second filling of the 19-gallon bucket. After that transfer of 5 gallons, the 19-gallon bucket contains the required 14 gallons.

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We don't know what your steps are supposed to look like, but we can write them as ...

(19-gallon bucket, 8 gallon bucket)

(0, 0) . . . start

(19, 0) . . . first fill

(11, 8) . . . first transfer

(11, 0) . . . first dump

(3, 8) . . . second transfer

(3, 0) . . . second dump

(0, 3) . . . third transfer

(19, 3) . . . second fill

(14, 8) . . . 4th transfer -- one bucket has 14 gallons in it

Optional:

(14, 0) . . . third dump -- one bucket has 14 gallons in it

throw the computer

step-by-step explanation:

pi x^2

step-by-step explanation:

pi times x squared