Glass bottles can be recycled. At one recycling center, 1 ton of clear glass is worth $25. (1 ton 2,000 pounds) 1. How many pounds of clear glass is worth $10? 2000 divided by 25 is 80 and 80 times 10 equal 800 mean 800 pounds i worth 10 2. How much money is 40 pounds of clear glass worth? 3. Write an equation to represent the relationship between the weight of clear glass and th value of the glass.

Glass bottles can be recycled. At one recycling center, 1 ton of clear glass is worth $25. (1 ton 2,000 pounds) 1. How many pounds of clear glass is worth $10? 2000 divided by 25 is 80 and 80 times 10 equal 800 mean 800 pounds i worth 10 2. How much money is 40 pounds of clear glass worth? 3. Write an equation to represent the relationship between the weight of clear glass and th value of the glass.

  1. 800 pounds; 2) $0.50; 3) v = 0.0125w.

Explanation

  1. Determine the value of 1 pound of clear glass. Since 1 ton (2,000 pounds) is worth $25, the value per pound is $$\frac{25}{2000} = 0.0125$$ dollars.
  2. To find how many pounds of clear glass is worth $10, set up the equation: $$0.0125 \times x = 10$$. Solving for $$x$$ gives $$x = \frac{10}{0.0125} = 800$$ pounds.
  3. To find how much money 40 pounds of clear glass is worth, use the value per pound: $$40 \times 0.0125 = 0.5$$ dollars.
  4. Write an equation to represent the relationship between the weight (w) of clear glass and its value (v): $$v = 0.0125w$$

This question focuses on understanding and applying proportional reasoning to solve problems involving the value of recycled glass. The core concept here is that the value of glass is directly proportional to its weight. You are given a rate: $25 for 1 ton (or 2000 pounds) of clear glass. To tackle the first part, you need to figure out how many pounds correspond to $10. Since $10 is a fraction of $25, the weight will be the same fraction of 2000 pounds. For the second part, you are given 40 pounds and need to find its value. You can use the established rate to calculate this. Finally, the question asks for an equation to represent this relationship. This means finding a formula that connects the weight (let’s call it ‘w’ in pounds) to the value (let’s call it ‘v’ in dollars). You’ll need to determine the value per pound and then express ‘v’ in terms of ‘w’. 


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