We are using one cup to pour water into an empty bottle. After pouring
2 cups of water, it weighs 360 grams, including the bottle. After pouring 5
cups of water, it weighs 600 grams including the bottle. What is the weight
of the empty bottle in grams?

To determine the weight of the empty bottle, we can set up a system of equations based on the given information.

Let's denote:
- \( B \) as the weight of the empty bottle in grams.
- \( W \) as the weight of one cup of water in grams.

From the problem, we have the following information:

1. After pouring 2 cups of water, the total weight is 360 grams:
\[ B + 2W = 360 \]

2. After pouring 5 cups of water, the total weight is 600 grams:
\[ B + 5W = 600 \]

We can solve this system of equations to find \( B \) and \( W \).

First, subtract the first equation from the second equation:
\[
(B + 5W) - (B + 2W) = 600 - 360
\]
\[
B + 5W - B - 2W = 240
\]
\[
3W = 240
\]
\[
W = \frac{240}{3} = 80
\]

Now that we know the weight of one cup of water (\( W \)), we can substitute \( W \) back into the first equation to find \( B \):
\[
B + 2W = 360
\]
\[
B + 2(80) = 360
\]
\[
B + 160 = 360
\]
\[
B = 360 - 160
\]
\[
B = 200
\]

Therefore, the weight of the empty bottle is \( \boxed{200} \) grams.

Would you like more details or have any questions?

Here are 8 related questions to further explore the topic:

1. If the weight of the bottle was 250 grams, what would be the weight of one cup of water given the same total weights after pouring 2 and 5 cups of water?
2. How would the total weight change if we poured 10 cups of water into the bottle?
3. If the bottle had an initial weight of 180 grams, what would the weight be after adding 7 cups of water?
4. What would the total weight be if we poured 3 cups of water into the bottle?
5. If each cup of water weighs 90 grams, what is the weight of the empty bottle?
6. How can we verify the calculations if the bottle's weight and the weight of one cup of water are given?
7. What would happen to the total weight if we added another 5 cups of water after the initial 5 cups?
8. How would the calculations change if the bottle's weight was given in kilograms instead of grams?

**Tip:** Always double-check your units when solving problems involving weights and measurements to ensure consistency and accuracy in your calculations.

Learn how to calculate the weight of an empty bottle using linear equations. Solve the problem where pouring 2 cups of water makes the total weight 360 grams, and pouring 5 cups of water makes it 600 grams including the bottle. Suitable for students in Grades 7-9.

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