When 2 dozen cans of food are placed in a bucket, the mass is 4560 g. When 18 cans of food are placed in the same bucket, the mass is 3480 g. Find the mass of the bucket?

X = wt. of each can 0f food,

Y = WT. OF each bucket,

24X + Y = 4560
18X + Y = 3480
Solve by elimination(subtract),
6X = 1080,
X = 180
Substitute 180 for X in 1st Eq:
24 * 180 + Y = 4560,
4320 + Y = 4560,
Y = 4560 - 4320 = 240 Grams.

240 Grams

240g

240 g

To find the mass of the bucket, we need to determine the difference in mass between the two scenarios when the cans of food are placed in the bucket.

When 2 dozen (which is equivalent to 24) cans of food are placed in the bucket, the mass is 4560 g.

When 18 cans of food are placed in the same bucket, the mass is 3480 g.

First, we calculate the mass of the cans alone in both scenarios:

Mass of 24 cans = 4560 g - Mass of the bucket

Mass of 18 cans = 3480 g - Mass of the bucket

Now, let's subtract the two equations:

(4560 g - Mass of the bucket) - (3480 g - Mass of the bucket) = (4560 g - 3480 g)

Mass of the cans cancels out, leaving us with:

Mass of the bucket - Mass of the bucket = 1080 g

Simplifying further:

0 = 1080 g

This is not a possible solution. Upon reviewing the problem, there seems to be an error or missing information. Please double-check the values given for the mass of the cans in each scenario.