# Jar Puzzle

There are multiple methods that can be used to solve this.

**Method 1: Algebra**

Let x = the weight of an empty jar

Let y = the weight of the contents of a full jar

We know that x + y = 120

Therefore, y = 120 – x

We also know that 2x + 0.5y = 150

Now, let’s plug one equation into the other and solve:

2x + 0.5(120 – x) = 150

2x + 60 – 0.5x = 150

1.5x = 90

x = 60

An empty jar weighs 60 grams.

**Method 2: Doubling**

- Double the right side.
- Now you know that 2 empty jars and 2 half-filled jars weigh 300 g in total.
- This means that 3 empty jars and 1 full jar weigh 300 g.
- From the left scale, you know that 1 full jar weighs 120 g.
- You now know that 3 empty jars weigh 300 g – 120 g = 180 g.
- Divide this by 3 to determine the weight of 1 empty jar: 60 g.

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