Sure! To solve percent problems using proportions, you'll typically set up a proportion that relates the part (the amount you're interested in) to the whole (the total amount) and the percent (the percentage out of 100). Here’s a quick guide on how to do that along with examples:
Steps to Solve Percent Problems with Proportions:
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Identify the Whole and the Part:
- The "whole" is the total amount.
- The "part" is the portion of the whole you're interested in.
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Set Up the Proportion: \[ \frac{\text{part}}{\text{whole}} = \frac{\text{percent}}{100} \]
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Cross-Multiply and Solve.
Example Problems:
Example 1: What is 20% of 50?
- Identify the Whole: The whole is 50.
- Identify the Percent: The percent is 20. In decimal, this represents 20/100.
- Set Up the Proportion:
\[ \frac{x}{50} = \frac{20}{100} \] - Cross-Multiply: \[ 100x = 20 \times 50 \] \[ 100x = 1000 \]
- Solve for x: \[ x = \frac{1000}{100} = 10 \]
Answer: 20% of 50 is 10.
Example 2: If you scored 15 out of 60 on a test, what percent did you score?
- Identify the Part: The part is 15 (your score).
- Identify the Whole: The whole is 60 (total points on the test).
- Set Up the Proportion:
\[ \frac{15}{60} = \frac{x}{100} \] - Cross-Multiply: \[ 15 \times 100 = 60x \] \[ 1500 = 60x \]
- Solve for x: \[ x = \frac{1500}{60} = 25 \]
Answer: You scored 25%.
Example 3: 30 is what percent of 150?
- Identify the Part: The part is 30.
- Identify the Whole: The whole is 150.
- Set Up the Proportion:
\[ \frac{30}{150} = \frac{x}{100} \] - Cross-Multiply: \[ 30 \times 100 = 150x \] \[ 3000 = 150x \]
- Solve for x: \[ x = \frac{3000}{150} = 20 \]
Answer: 30 is 20% of 150.
Practice Problems:
- What is 40% of 200?
- If you read 25 pages out of 100, what percent of the book did you read?
- 45 is what percent of 180?
Feel free to try these practice problems, and let me know if you need any help with them!
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