Question

leo has a balance, and hes 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.
how much does each wooden block weigh?
simplify any fractions.
\boxed{} ounces

Explanation:

Step1: Define variable for block weight

Let \( x \) be the weight of one wooden block (in ounces).

Step2: Set up equation from balance

The left side (6 blocks + 200 - ounce weight) is \( 6x + 200 \), and the right side (2 blocks + 500 - ounce weight) is \( 2x + 500 \). Since the balance is equal:

$$ 6x + 200 = 2x + 500 $$

Step3: Subtract \( 2x \) from both sides

$$ 6x - 2x + 200 = 2x - 2x + 500 $$

$$ 4x + 200 = 500 $$

Step4: Subtract 200 from both sides

$$ 4x + 200 - 200 = 500 - 200 $$

$$ 4x = 300 $$

Step5: Divide both sides by 4

$$ x = \frac{300}{4} = 75 $$

Answer:

75