Ratio and Proportions - Free worksheets for ratio word problems - Free Printable

Problem Solving: Ratios Word Problems

The worksheet contains several ratio-based word problems. Below, I will solve each problem step by step and explain the solution.

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#### Problem 1:
The ratio of boys to girls in a classroom is 7 to 11. If there are a total of 49 boys in the classroom, then how many boys and girls are there altogether?

Solution:
1. The ratio of boys to girls is given as \( 7 : 11 \).
2. Let the number of boys be \( 7x \) and the number of girls be \( 11x \), where \( x \) is a common multiplier.
3. We are told there are 49 boys:
\[
7x = 49
\]
4. Solve for \( x \):
\[
x = \frac{49}{7} = 7
\]
5. Now, calculate the number of girls:
\[
11x = 11 \times 7 = 77
\]
6. The total number of students (boys + girls) is:
\[
49 + 77 = 126
\]

Answer:
\[
\boxed{126}
\]

---

#### Problem 2:
The ratio of marbles to stones in a large pot is 6 to 7. If there are 42 marbles, then how many stones are there?

Solution:
1. The ratio of marbles to stones is given as \( 6 : 7 \).
2. Let the number of marbles be \( 6x \) and the number of stones be \( 7x \), where \( x \) is a common multiplier.
3. We are told there are 42 marbles:
\[
6x = 42
\]
4. Solve for \( x \):
\[
x = \frac{42}{6} = 7
\]
5. Now, calculate the number of stones:
\[
7x = 7 \times 7 = 49
\]

Answer:
\[
\boxed{49}
\]

---

#### Problem 3:
The ratio of coins to notes in a bag is 3 to 8. If there are a total of 24 coins, then how many notes are there?

Solution:
1. The ratio of coins to notes is given as \( 3 : 8 \).
2. Let the number of coins be \( 3x \) and the number of notes be \( 8x \), where \( x \) is a common multiplier.
3. We are told there are 24 coins:
\[
3x = 24
\]
4. Solve for \( x \):
\[
x = \frac{24}{3} = 8
\]
5. Now, calculate the number of notes:
\[
8x = 8 \times 8 = 64
\]

Answer:
\[
\boxed{64}
\]

---

#### Problem 4:
The ratio of black bags to blue bags is 5 to 3. If there are a total of 10 black bags, then how many blue bags are there?

Solution:
1. The ratio of black bags to blue bags is given as \( 5 : 3 \).
2. Let the number of black bags be \( 5x \) and the number of blue bags be \( 3x \), where \( x \) is a common multiplier.
3. We are told there are 10 black bags:
\[
5x = 10
\]
4. Solve for \( x \):
\[
x = \frac{10}{5} = 2
\]
5. Now, calculate the number of blue bags:
\[
3x = 3 \times 2 = 6
\]

Answer:
\[
\boxed{6}
\]

---

#### Problem 5:
The ratio of trucks to cars is 7 to 8. If there are a total of 21 trucks, how many cars are there?

Solution:
1. The ratio of trucks to cars is given as \( 7 : 8 \).
2. Let the number of trucks be \( 7x \) and the number of cars be \( 8x \), where \( x \) is a common multiplier.
3. We are told there are 21 trucks:
\[
7x = 21
\]
4. Solve for \( x \):
\[
x = \frac{21}{7} = 3
\]
5. Now, calculate the number of cars:
\[
8x = 8 \times 3 = 24
\]

Answer:
\[
\boxed{24}
\]

---

#### Problem 6:
The ratio of red ribbons to green ribbons is 4 to 6. If there are a total of 32 red ribbons, then how many green ribbons are there?

Solution:
1. The ratio of red ribbons to green ribbons is given as \( 4 : 6 \). This can be simplified to \( 2 : 3 \) (by dividing both terms by 2).
2. Let the number of red ribbons be \( 2x \) and the number of green ribbons be \( 3x \), where \( x \) is a common multiplier.
3. We are told there are 32 red ribbons:
\[
2x = 32
\]
4. Solve for \( x \):
\[
x = \frac{32}{2} = 16
\]
5. Now, calculate the number of green ribbons:
\[
3x = 3 \times 16 = 48
\]

Answer:
\[
\boxed{48}
\]

---

#### Problem 7:
The volume of water in two containers is in the ratio of 6 to 7. If the volume of the first container is 36 liters, find the volume of the second container.

Solution:
1. The ratio of the volumes of the two containers is given as \( 6 : 7 \).
2. Let the volume of the first container be \( 6x \) and the volume of the second container be \( 7x \), where \( x \) is a common multiplier.
3. We are told the volume of the first container is 36 liters:
\[
6x = 36
\]
4. Solve for \( x \):
\[
x = \frac{36}{6} = 6
\]
5. Now, calculate the volume of the second container:
\[
7x = 7 \times 6 = 42
\]

Answer:
\[
\boxed{42}
\]

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Final Answers:

1. \(\boxed{126}\)
2. \(\boxed{49}\)
3. \(\boxed{64}\)
4. \(\boxed{6}\)
5. \(\boxed{24}\)
6. \(\boxed{48}\)
7. \(\boxed{42}\)