Question

An empty container has a mass of 600 grams. When 8 cans of equal mass are put into the container, the filled container has a mass of 7 kilograms. What is the mass of each can in grams?

Answer 1

To find the mass of each can, let's set up the problem with the information given:

1. The mass of the empty container is 600 grams.
2. The total mass of the filled container (container plus the cans) is 7 kilograms.

First, convert 7 kilograms to grams:

\[
7 \text{ kg} = 7 \times 1000 = 7000 \text{ grams}
\]

Next, let \( m \) be the mass of each can in grams. Since there are 8 cans, the total mass of the cans is:

\[
8m
\]

Now, we can express the total mass of the filled container as the sum of the mass of the container and the mass of the cans:

\[
\text{Total mass} = \text{mass of container} + \text{mass of cans}
\]
\[
7000 = 600 + 8m
\]

To find \( 8m \), we first subtract the mass of the container from the total mass:

\[
7000 - 600 = 8m
\]
\[
6400 = 8m
\]

Now, solve for \( m \) by dividing both sides by 8:

\[
m = \frac{6400}{8} = 800
\]

Thus, the mass of each can is:

\[
\boxed{800} \text{ grams}
\]