Question

solve percent problems whith proportions quick check

Answer 1

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:

1. **Identify the percent problem**: Determine the whole amount and the part you need to find.

2. **Set up the proportion**: Use the formula:
\[
\frac{\text{part}}{\text{whole}} = \frac{\text{percent}}{100}
\]

3. **Cross-multiply**: This allows you to solve for the unknown.

4. **Solve for the unknown**.

### Example Problems:

1. **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**.

2. **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**.

3. **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!