Leo has a balance, and he's playing around with some weights and wooden blocks. He eventually gets the two sides to balance with 6 blocks and a 200-ounce weight on one side and 2 blocks and a 500-ounce weight on the other side.

Question

How much does each wooden block weigh?
Simplify any fractions.
ounces

Answer 1

To solve the problem, we can set up an equation based on the information given about the balance.

Let \( b \) represent the weight of each wooden block in ounces.

From the problem statement, we know that:

On one side of the balance:

• 6 blocks weigh \( 6b \) ounces
• Plus a 200-ounce weight makes it \( 6b + 200 \) ounces.

On the other side of the balance:

• 2 blocks weigh \( 2b \) ounces
• Plus a 500-ounce weight makes it \( 2b + 500 \) ounces.

Since the balance is even, we can set the two sides equal to each other:

\[ 6b + 200 = 2b + 500 \]

Now, we can solve for \( b \):

1. Subtract \( 2b \) from both sides: \[ 6b - 2b + 200 = 500 \] \[ 4b + 200 = 500 \]

2. Subtract 200 from both sides: \[ 4b = 300 \]

3. Divide both sides by 4: \[ b = \frac{300}{4} = 75 \]

Thus, each wooden block weighs 75 ounces.