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.How much does each wooden block weigh?Simplify any fractions. ounces
Question
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.How much does each wooden block weigh?Simplify any fractions. ounces
Solution
Let's solve this step by step:
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First, let's denote the weight of each wooden block as 'x'.
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According to the problem, we have two equations based on the balance. The weight on both sides of the balance is equal, so we can write the equations as:
6x + 200 = 2x + 500
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Now, let's solve this equation for 'x'. Start by subtracting 2x from both sides:
6x - 2x = 500 - 200 4x = 300
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Finally, divide both sides by 4 to solve for 'x':
x = 300 / 4 x = 75
So, each wooden block weighs 75 ounces.
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