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Answer :
- To find 30% of what number equals 15, divide 15 by 0.30, resulting in 50.
- To determine what percent of 52 is 20, divide 20 by 52 and multiply by 100, which is approximately 38.46%.
- To find 120% of 70, multiply 70 by 1.20, resulting in 84.
- To find the number for which 48 is 75%, divide 48 by 0.75, resulting in 64.
$\boxed{50, 38.46, 84, 64}$
### Explanation
1. Introduction
We will solve each percentage problem step by step.
2. Solving Problem 7
**Problem 7:** 15 is 30% of what number?
Let $x$ be the number we are looking for. We can write the equation:
$$0.30 \times x = 15$$
To solve for $x$, we divide both sides by 0.30:
$$x = \frac{15}{0.30} = 50$$
So, 15 is 30% of 50.
3. Solving Problem 9
**Problem 9:** 20 is what percent of 52?
Let $p$ be the percentage we are looking for. We can write the equation:
$$\frac{p}{100} \times 52 = 20$$
To solve for $p$, we multiply both sides by 100 and divide by 52:
$$p = \frac{20 \times 100}{52} = \frac{2000}{52} \approx 38.46$$
So, 20 is approximately 38.46% of 52.
4. Solving Problem 8
**Problem 8:** What number is 120% of 70?
Let $y$ be the number we are looking for. We can write the equation:
$$y = 1.20 \times 70$$
$$y = 84$$
So, 120% of 70 is 84.
5. Solving Problem 10
**Problem 10:** 48 is 75% of what number?
Let $z$ be the number we are looking for. We can write the equation:
$$0.75 \times z = 48$$
To solve for $z$, we divide both sides by 0.75:
$$z = \frac{48}{0.75} = 64$$
So, 48 is 75% of 64.
6. Final Answers
Here are the answers to the problems:
7. 50
8. 84
9. 38.46
10. 64
### Examples
Understanding percentages is crucial in everyday life. For example, when shopping, you often encounter discounts expressed as percentages. Calculating the sale price involves finding a percentage of the original price and subtracting it. Similarly, understanding interest rates on loans or investments requires working with percentages. Whether it's calculating tips at a restaurant or understanding tax rates, percentages are fundamental in financial literacy and decision-making.
- To determine what percent of 52 is 20, divide 20 by 52 and multiply by 100, which is approximately 38.46%.
- To find 120% of 70, multiply 70 by 1.20, resulting in 84.
- To find the number for which 48 is 75%, divide 48 by 0.75, resulting in 64.
$\boxed{50, 38.46, 84, 64}$
### Explanation
1. Introduction
We will solve each percentage problem step by step.
2. Solving Problem 7
**Problem 7:** 15 is 30% of what number?
Let $x$ be the number we are looking for. We can write the equation:
$$0.30 \times x = 15$$
To solve for $x$, we divide both sides by 0.30:
$$x = \frac{15}{0.30} = 50$$
So, 15 is 30% of 50.
3. Solving Problem 9
**Problem 9:** 20 is what percent of 52?
Let $p$ be the percentage we are looking for. We can write the equation:
$$\frac{p}{100} \times 52 = 20$$
To solve for $p$, we multiply both sides by 100 and divide by 52:
$$p = \frac{20 \times 100}{52} = \frac{2000}{52} \approx 38.46$$
So, 20 is approximately 38.46% of 52.
4. Solving Problem 8
**Problem 8:** What number is 120% of 70?
Let $y$ be the number we are looking for. We can write the equation:
$$y = 1.20 \times 70$$
$$y = 84$$
So, 120% of 70 is 84.
5. Solving Problem 10
**Problem 10:** 48 is 75% of what number?
Let $z$ be the number we are looking for. We can write the equation:
$$0.75 \times z = 48$$
To solve for $z$, we divide both sides by 0.75:
$$z = \frac{48}{0.75} = 64$$
So, 48 is 75% of 64.
6. Final Answers
Here are the answers to the problems:
7. 50
8. 84
9. 38.46
10. 64
### Examples
Understanding percentages is crucial in everyday life. For example, when shopping, you often encounter discounts expressed as percentages. Calculating the sale price involves finding a percentage of the original price and subtracting it. Similarly, understanding interest rates on loans or investments requires working with percentages. Whether it's calculating tips at a restaurant or understanding tax rates, percentages are fundamental in financial literacy and decision-making.
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