Worksheet demonstrating how to read triple and four beam balances for measuring mass.

To solve the problem of determining the masses shown on each of the beam balances, we need to carefully analyze the positions of the sliding weights on the beams. Let's break it down step by step for each balance.

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Triple Beam Balance

#### 1. First Triple Beam Balance
- Hundreds Beam: The weight is at the 60 mark.
- Tens Beam: The weight is at the 30 mark.
- Ones Beam: The weight is at the 4 mark (on the rider scale).

The total mass is:
\[
60 + 30 + 4 = 94 \text{ grams}
\]

#### 2. Second Triple Beam Balance
- Hundreds Beam: The weight is at the 40 mark.
- Tens Beam: The weight is at the 50 mark.
- Ones Beam: The weight is at the 7 mark (on the rider scale).

The total mass is:
\[
40 + 50 + 7 = 97 \text{ grams}
\]

#### 3. Third Triple Beam Balance
- Hundreds Beam: The weight is at the 80 mark.
- Tens Beam: The weight is at the 20 mark.
- Ones Beam: The weight is at the 3 mark (on the rider scale).

The total mass is:
\[
80 + 20 + 3 = 103 \text{ grams}
\]

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Four Beam Balance

#### 1. Four Beam Balance
- Thousands Beam: The weight is at the 0 mark.
- Hundreds Beam: The weight is at the 500 mark.
- Tens Beam: The weight is at the 70 mark.
- Ones Beam: The weight is at the 6 mark (on the rider scale).

The total mass is:
\[
500 + 70 + 6 = 576 \text{ grams}
\]

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Final Answers

1. First Triple Beam Balance: \( \boxed{94} \) grams
2. Second Triple Beam Balance: \( \boxed{97} \) grams
3. Third Triple Beam Balance: \( \boxed{103} \) grams
4. Four Beam Balance: \( \boxed{576} \) grams

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Explanation

- Triple Beam Balance: It has three beams (hundreds, tens, and ones), and the rider scale provides precision in the ones place.
- Four Beam Balance: It has four beams (thousands, hundreds, tens, and ones), and the rider scale provides precision in the ones place.
- To find the total mass, add the values from each beam and the rider scale.

This method ensures accurate reading of the masses shown on the balances.