Ratio and Proportion Word Problems Worksheet 1

Let's solve each problem step by step:

---

Problem 1:

A Java book is comprised of two sections: core and advanced Java in the ratio 7:2. How much of each type of content will be needed to make a book of 450 pages?

#### Solution:
1. The ratio of core to advanced Java is 7:2.
2. Let the number of pages for core Java be \( 7x \) and for advanced Java be \( 2x \).
3. The total number of pages is given as 450:
\[
7x + 2x = 450
\]
4. Simplify the equation:
\[
9x = 450
\]
5. Solve for \( x \):
\[
x = \frac{450}{9} = 50
\]
6. Calculate the number of pages for each section:
- Core Java: \( 7x = 7 \times 50 = 350 \)
- Advanced Java: \( 2x = 2 \times 50 = 100 \)

#### Answer:
\[
\boxed{350 \text{ pages for core Java, } 100 \text{ pages for advanced Java}}
\]

---

Problem 2:

30 girls and boys have planned for a picnic. There is a ratio of 3 girls to 7 boys. How many boys are there?

#### Solution:
1. The ratio of girls to boys is 3:7.
2. Let the number of girls be \( 3x \) and the number of boys be \( 7x \).
3. The total number of children is given as 30:
\[
3x + 7x = 30
\]
4. Simplify the equation:
\[
10x = 30
\]
5. Solve for \( x \):
\[
x = \frac{30}{10} = 3
\]
6. Calculate the number of boys:
\[
7x = 7 \times 3 = 21
\]

#### Answer:
\[
\boxed{21}
\]

---

Problem 3:

12 miles is approximately equal to 6 km. How many km are equal to 18 miles? How many miles are equal to 42 km?

#### Solution:
1. Convert 18 miles to km:
- Given: 12 miles = 6 km.
- Therefore, 1 mile = \( \frac{6}{12} = 0.5 \) km.
- For 18 miles:
\[
18 \text{ miles} = 18 \times 0.5 \text{ km} = 9 \text{ km}
\]

2. Convert 42 km to miles:
- Given: 6 km = 12 miles.
- Therefore, 1 km = \( \frac{12}{6} = 2 \) miles.
- For 42 km:
\[
42 \text{ km} = 42 \times 2 \text{ miles} = 84 \text{ miles}
\]

#### Answers:
\[
\boxed{9 \text{ km for 18 miles, } 84 \text{ miles for 42 km}}
\]

---

Problem 4:

5 pizzas cost $60. What will 9 pizzas cost?

#### Solution:
1. Cost of 1 pizza:
\[
\text{Cost of 1 pizza} = \frac{60}{5} = 12 \text{ dollars}
\]
2. Cost of 9 pizzas:
\[
\text{Cost of 9 pizzas} = 9 \times 12 = 108 \text{ dollars}
\]

#### Answer:
\[
\boxed{108}
\]

---

Problem 5:

6 stuffed peppers cost $36. What will 12 stuffed peppers cost?

#### Solution:
1. Cost of 1 stuffed pepper:
\[
\text{Cost of 1 stuffed pepper} = \frac{36}{6} = 6 \text{ dollars}
\]
2. Cost of 12 stuffed peppers:
\[
\text{Cost of 12 stuffed peppers} = 12 \times 6 = 72 \text{ dollars}
\]

#### Answer:
\[
\boxed{72}
\]

---

Problem 6:

Mr. Jeff divided his money in the ratio 4:2 between Jon and Jack. Jon got the smaller amount of $1,256. How much did Jack receive?

#### Solution:
1. The ratio of Jon's share to Jack's share is 4:2, which simplifies to 2:1.
2. Let Jon's share be \( 2x \) and Jack's share be \( x \).
3. Jon's share is given as $1,256:
\[
2x = 1256
\]
4. Solve for \( x \):
\[
x = \frac{1256}{2} = 628
\]
5. Jack's share is \( x \):
\[
\text{Jack's share} = 628 \text{ dollars}
\]

#### Answer:
\[
\boxed{628}
\]

---

Problem 7:

3:4 = 15:20. True OR False?

#### Solution:
1. Simplify the ratio 15:20:
\[
\frac{15}{20} = \frac{3}{4}
\]
2. Since \( 3:4 = 15:20 \), the statement is true.

#### Answer:
\[
\boxed{\text{True}}
\]

---

Problem 8:

2:5 and 30:20 are equal ratios. True OR False?

#### Solution:
1. Simplify the ratio 30:20:
\[
\frac{30}{20} = \frac{3}{2}
\]
2. Compare \( 2:5 \) and \( 3:2 \):
- \( 2:5 \neq 3:2 \)
3. The statement is false.

#### Answer:
\[
\boxed{\text{False}}
\]

---

Problem 9:

3:4 = 6:8? True OR False?

#### Solution:
1. Simplify the ratio 6:8:
\[
\frac{6}{8} = \frac{3}{4}
\]
2. Since \( 3:4 = 6:8 \), the statement is true.

#### Answer:
\[
\boxed{\text{True}}
\]

---

Problem 10:

10 glasses cost 40 dollars. How much do 20 glasses cost?

#### Solution:
1. Cost of 1 glass:
\[
\text{Cost of 1 glass} = \frac{40}{10} = 4 \text{ dollars}
\]
2. Cost of 20 glasses:
\[
\text{Cost of 20 glasses} = 20 \times 4 = 80 \text{ dollars}
\]

#### Answer:
\[
\boxed{80}
\]

---

Final Answers:

1. \(\boxed{350 \text{ pages for core Java, } 100 \text{ pages for advanced Java}}\)
2. \(\boxed{21}\)
3. \(\boxed{9 \text{ km for 18 miles, } 84 \text{ miles for 42 km}}\)
4. \(\boxed{108}\)
5. \(\boxed{72}\)
6. \(\boxed{628}\)
7. \(\boxed{\text{True}}\)
8. \(\boxed{\text{False}}\)
9. \(\boxed{\text{True}}\)
10. \(\boxed{80}\)