Percentages Problems Worksheet No.5 | Worksheets | Math Center - Free Printable

Let's solve each problem step by step from the Percentage Problems Worksheet 5.

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1. On a math test there are 40 questions. 20% of the questions are division drills. How many division drills on the test?

Step 1: Find 20% of 40.

$$
20\% \text{ of } 40 = \frac{20}{100} \times 40 = 0.2 \times 40 = 8
$$

✔ Answer: 8 division drills

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2. Watermelon contains 85% water.

#### a. How much water will be in a watermelon of 5kg?

Step 1: 85% of 5 kg is water.

$$
85\% \text{ of } 5 = \frac{85}{100} \times 5 = 0.85 \times 5 = 4.25 \text{ kg}
$$

✔ Answer: 4.25 kg of water

#### b. What percentage of substance makes up the rest of the watermelon?

Since 85% is water, the remaining part is:

$$
100\% - 85\% = 15\%
$$

✔ Answer: 15%

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3. The sum of two numbers is 100. The first number is 60% of the sum.

#### a. What percent of the sum is the second number?

- First number = 60% of 100 = 60
- So, second number = 100 - 60 = 40
- Percent of the sum that the second number is:

$$
\frac{40}{100} \times 100\% = 40\%
$$

✔ Answer: 40%

#### b. Find the numbers.

We already found:
- First number = 60
- Second number = 40

✔ Answer: 60 and 40

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4. An engine factory manufactures 36,000 engines in a year. $\frac{1}{4}$ of them are sold locally, 30% are exported, and the rest are installed in cars.

Total engines = 36,000

#### a. How many engines are sold locally?

$$
\frac{1}{4} \times 36,000 = 9,000
$$

✔ Answer: 9,000 engines

#### b. How many engines are exported?

30% of 36,000:

$$
0.30 \times 36,000 = 10,800
$$

✔ Answer: 10,800 engines

#### c. How many engines are installed in cars?

Total used = Local + Exported + Installed

So:

$$
\text{Installed} = 36,000 - (9,000 + 10,800) = 36,000 - 19,800 = 16,200
$$

✔ Answer: 16,200 engines

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5. In the school’s library there are 10,000 books. 2000 of the books are for the first and second grade, 4500 are for the third and fourth grade, and the remaining are for the fifth and sixth grade.

Total books = 10,000
First & second grade = 2,000
Third & fourth grade = 4,500
Fifth & sixth grade = ?

#### a. What percentage of books are for the first and second grade?

$$
\frac{2000}{10000} \times 100\% = 20\%
$$

✔ Answer: 20%

#### b. What percentage of books are for the third and fourth grade?

$$
\frac{4500}{10000} \times 100\% = 45\%
$$

✔ Answer: 45%

#### c. What percentage of books are for the fifth and sixth grade?

First, find how many books are left:

$$
10,000 - (2,000 + 4,500) = 3,500
$$

Now calculate percentage:

$$
\frac{3500}{10000} \times 100\% = 35\%
$$

✔ Answer: 35%

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✔ Final Answers Summary:

#### 1. 8 division drills
#### 2a. 4.25 kg of water
#### 2b. 15%
#### 3a. 40%
#### 3b. 60 and 40
#### 4a. 9,000 engines sold locally
#### 4b. 10,800 engines exported
#### 4c. 16,200 engines installed in cars
#### 5a. 20%
#### 5b. 45%
#### 5c. 35%

Let me know if you'd like this as a printable solution sheet!