Ratio Worksheets | Free - Distance Learning, worksheets and more ... - Free Printable

Problem Solving: Understanding Ratios

We will solve each problem step by step, using the concept of ratios.

---

#### 1) A classroom had 35 glue sticks. If the ratio of glue sticks to glue bottles was 5 : 2, how many glue bottles did the classroom have?

- Given:
- Total glue sticks = 35
- Ratio of glue sticks to glue bottles = 5 : 2

- Solution:
- Let the number of glue sticks be \( 5x \) and the number of glue bottles be \( 2x \).
- According to the problem, \( 5x = 35 \).
- Solve for \( x \):
\[
x = \frac{35}{5} = 7
\]
- The number of glue bottles is \( 2x \):
\[
2x = 2 \times 7 = 14
\]

- Answer:
\[
\boxed{14}
\]

---

#### 2) A student finished 8 of her homework problems in class. If the ratio of the problems she finished to problems she still had left was 4 : 1, how many homework problems did she have total?

- Given:
- Problems finished = 8
- Ratio of finished problems to remaining problems = 4 : 1

- Solution:
- Let the number of finished problems be \( 4x \) and the number of remaining problems be \( x \).
- According to the problem, \( 4x = 8 \).
- Solve for \( x \):
\[
x = \frac{8}{4} = 2
\]
- The total number of problems is the sum of finished and remaining problems:
\[
\text{Total problems} = 4x + x = 5x = 5 \times 2 = 10
\]

- Answer:
\[
\boxed{10}
\]

---

#### 3) On a Saturday, a library checked out 52 books. If 24 of the books were fiction, what is the ratio of non-fiction books to fiction books checked out?

- Given:
- Total books checked out = 52
- Fiction books = 24

- Solution:
- Non-fiction books = Total books - Fiction books:
\[
\text{Non-fiction books} = 52 - 24 = 28
\]
- The ratio of non-fiction books to fiction books is:
\[
\text{Ratio} = \frac{\text{Non-fiction books}}{\text{Fiction books}} = \frac{28}{24}
\]
- Simplify the ratio by dividing both terms by their greatest common divisor (GCD), which is 4:
\[
\frac{28}{24} = \frac{28 \div 4}{24 \div 4} = \frac{7}{6}
\]

- Answer:
\[
\boxed{7 : 6}
\]

---

#### 4) A recipe called for the ratio of sugar to flour to be 10 : 3. If you used 70 ounce of sugar, how many ounces of flour would you need to use?

- Given:
- Ratio of sugar to flour = 10 : 3
- Sugar used = 70 ounces

- Solution:
- Let the amount of sugar be \( 10x \) and the amount of flour be \( 3x \).
- According to the problem, \( 10x = 70 \).
- Solve for \( x \):
\[
x = \frac{70}{10} = 7
\]
- The amount of flour needed is \( 3x \):
\[
3x = 3 \times 7 = 21
\]

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

---

#### 5) At a bake sale there were 72 raisin cookies sold. If the ratio of raisin cookies sold to oatmeal cookies sold was 9 : 1, what is the combined amount of raisin and oatmeal cookies sold?

- Given:
- Raisin cookies sold = 72
- Ratio of raisin cookies to oatmeal cookies = 9 : 1

- Solution:
- Let the number of raisin cookies be \( 9x \) and the number of oatmeal cookies be \( x \).
- According to the problem, \( 9x = 72 \).
- Solve for \( x \):
\[
x = \frac{72}{9} = 8
\]
- The number of oatmeal cookies sold is \( x \):
\[
x = 8
\]
- The combined amount of raisin and oatmeal cookies sold is:
\[
\text{Combined total} = 9x + x = 10x = 10 \times 8 = 80
\]

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

---

#### 6) Kaleb had 136 songs on his MP3 player. If he deleted 56 songs, what is the ratio of songs he kept to songs he deleted?

- Given:
- Total songs = 136
- Songs deleted = 56

- Solution:
- Songs kept = Total songs - Songs deleted:
\[
\text{Songs kept} = 136 - 56 = 80
\]
- The ratio of songs kept to songs deleted is:
\[
\text{Ratio} = \frac{\text{Songs kept}}{\text{Songs deleted}} = \frac{80}{56}
\]
- Simplify the ratio by dividing both terms by their greatest common divisor (GCD), which is 8:
\[
\frac{80}{56} = \frac{80 \div 8}{56 \div 8} = \frac{10}{7}
\]

- Answer:
\[
\boxed{10 : 7}
\]

---

#### 7) The ratio of red cars to blue cars in a parking lot was 5 : 3. If there were 40 red cars, how many blue cars were there?

- Given:
- Ratio of red cars to blue cars = 5 : 3
- Red cars = 40

- Solution:
- Let the number of red cars be \( 5x \) and the number of blue cars be \( 3x \).
- According to the problem, \( 5x = 40 \).
- Solve for \( x \):
\[
x = \frac{40}{5} = 8
\]
- The number of blue cars is \( 3x \):
\[
3x = 3 \times 8 = 24
\]

- Answer:
\[
\boxed{24}
\]

---

#### 8) A produce store sold 63 red apples. If the ratio of red apples to green apples sold was 7 : 2, what is the combined amount of red and green apples sold?

- Given:
- Red apples sold = 63
- Ratio of red apples to green apples = 7 : 2

- Solution:
- Let the number of red apples be \( 7x \) and the number of green apples be \( 2x \).
- According to the problem, \( 7x = 63 \).
- Solve for \( x \):
\[
x = \frac{63}{7} = 9
\]
- The number of green apples sold is \( 2x \):
\[
2x = 2 \times 9 = 18
\]
- The combined amount of red and green apples sold is:
\[
\text{Combined total} = 7x + 2x = 9x = 9 \times 9 = 81
\]

- Answer:
\[
\boxed{81}
\]

---

#### 9) For homework, a student had to complete 15 problems total. If she finished 6 problems in class, what is the ratio of problems she still needs to complete to problems that she’s already finished?

- Given:
- Total problems = 15
- Problems finished = 6

- Solution:
- Problems remaining = Total problems - Problems finished:
\[
\text{Problems remaining} = 15 - 6 = 9
\]
- The ratio of problems remaining to problems finished is:
\[
\text{Ratio} = \frac{\text{Problems remaining}}{\text{Problems finished}} = \frac{9}{6}
\]
- Simplify the ratio by dividing both terms by their greatest common divisor (GCD), which is 3:
\[
\frac{9}{6} = \frac{9 \div 3}{6 \div 3} = \frac{3}{2}
\]

- Answer:
\[
\boxed{3 : 2}
\]

---

#### 10) At a farm the ratio of cows to horses was 9 : 2. If there were 72 cows at the farm, how many horses were there?

- Given:
- Ratio of cows to horses = 9 : 2
- Cows = 72

- Solution:
- Let the number of cows be \( 9x \) and the number of horses be \( 2x \).
- According to the problem, \( 9x = 72 \).
- Solve for \( x \):
\[
x = \frac{72}{9} = 8
\]
- The number of horses is \( 2x \):
\[
2x = 2 \times 8 = 16
\]

- Answer:
\[
\boxed{16}
\]

---

Final Answers:

1. \(\boxed{14}\)
2. \(\boxed{10}\)
3. \(\boxed{7 : 6}\)
4. \(\boxed{21}\)
5. \(\boxed{80}\)
6. \(\boxed{10 : 7}\)
7. \(\boxed{24}\)
8. \(\boxed{81}\)
9. \(\boxed{3 : 2}\)
10. \(\boxed{16}\)