What is the mass of the bucket?

Question

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

Answer 1

For this problem there are two equations, let x = the mass of one can of food and let b= the mass of the bucket

24x + b = 4560g

18x +b = 3480g 

use the second equation to find the value of b: b = 3480g - 18x

substitute this equation into the first equation: 24x + (3480g - 18x) = 4560g

Simplify: 6x = 1080g

x = 180g, plug in x to the first equation to find b

24(180g) + b = 4560g

b = 240g