Sure! To solve percent problems using proportions, you can set up a simple equation based on the relationship between part, whole, and percent. Here's a quick guide on how to do it:
Steps to Solve Percent Problems with Proportions:
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Identify the percent problem: Determine the whole amount and the part you need to find.
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Set up the proportion: Use the formula: \[ \frac{\text{part}}{\text{whole}} = \frac{\text{percent}}{100} \]
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Cross-multiply: This allows you to solve for the unknown.
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Solve for the unknown.
Example Problems:
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What is 20% of 50?
- Whole = 50
- Percent = 20%
- Set up the proportion: \[ \frac{x}{50} = \frac{20}{100} \]
- Cross-multiply: \[ 100x = 20 \times 50 \]
- Solve: \[ x = \frac{1000}{100} = 10 \] Thus, 20% of 50 is 10.
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If 30 is 60% of what number?
- Part = 30
- Percent = 60%
- Set up the proportion: \[ \frac{30}{x} = \frac{60}{100} \]
- Cross-multiply: \[ 60x = 3000 \]
- Solve: \[ x = \frac{3000}{60} = 50 \] Thus, 30 is 60% of 50.
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What percent is 75 of 300?
- Part = 75
- Whole = 300
- Set up the proportion: \[ \frac{75}{300} = \frac{x}{100} \]
- Cross-multiply: \[ 75 \times 100 = 300x \]
- Solve: \[ 7500 = 300x \implies x = \frac{7500}{300} = 25 \] Thus, 75 is 25% of 300.
Quick Tips:
- Always convert your percent to a fraction (percent/100) in the proportion.
- Ensure to isolate the variable you are solving for and simplify your results.
By following these simple steps, you can quickly solve percent problems using proportions!
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