Students can sharpen their math skills by working through these ten ratio-based scenarios, such as calculating paint times and mixing smoothies.

Grade 7 Ratio Word Problems

Here are the solutions to the problems provided in the image, along with detailed explanations:

---

#### 1. Recipe Scaling
Problem: A cookie recipe makes 24 cookies using 2 cups of flour. How much flour is needed to make 36 cookies?

Solution:
- The ratio of cookies to flour is given as \( \frac{24 \text{ cookies}}{2 \text{ cups of flour}} \).
- We need to find how much flour is required for 36 cookies.
- Set up a proportion:
\[
\frac{24 \text{ cookies}}{2 \text{ cups of flour}} = \frac{36 \text{ cookies}}{x \text{ cups of flour}}
\]
- Cross-multiply to solve for \( x \):
\[
24x = 36 \times 2
\]
\[
24x = 72
\]
\[
x = \frac{72}{24} = 3
\]

Answer: \( \boxed{3} \) cups of flour.

---

#### 2. Painting Time
Problem: It takes 4 hours for 8 painters to complete a mural. How many hours will it take for 10 painters to complete the same mural?

Solution:
- First, calculate the total painter-hours required to complete the mural:
\[
\text{Total painter-hours} = 8 \text{ painters} \times 4 \text{ hours} = 32 \text{ painter-hours}
\]
- If 10 painters work together, the time \( t \) required can be found by dividing the total painter-hours by the number of painters:
\[
t = \frac{32 \text{ painter-hours}}{10 \text{ painters}} = 3.2 \text{ hours}
\]

Answer: \( \boxed{3.2} \) hours.

---

#### 3. Proportional Relationships
Problem: The ratio of the number of miles driven to the number of gallons of gas used is 30:2. How many gallons of gas would be used to drive 60 miles?

Solution:
- The ratio of miles to gallons is \( \frac{30 \text{ miles}}{2 \text{ gallons}} \).
- We need to find how many gallons are used for 60 miles.
- Set up a proportion:
\[
\frac{30 \text{ miles}}{2 \text{ gallons}} = \frac{60 \text{ miles}}{x \text{ gallons}}
\]
- Cross-multiply to solve for \( x \):
\[
30x = 60 \times 2
\]
\[
30x = 120
\]
\[
x = \frac{120}{30} = 4
\]

Answer: \( \boxed{4} \) gallons.

---

#### 4. Fruit Smoothies
Problem: A smoothie recipe calls for a ratio of 2 cups of strawberries to 3 cups of yogurt. If you want to make 6 cups of smoothie, how many cups of yogurt should you use?

Solution:
- The total parts in the ratio are \( 2 + 3 = 5 \).
- Each part represents:
\[
\frac{6 \text{ cups}}{5} = 1.2 \text{ cups per part}
\]
- The amount of yogurt (3 parts) is:
\[
3 \times 1.2 = 3.6 \text{ cups}
\]

Answer: \( \boxed{3.6} \) cups of yogurt.

---

#### 5. Train Speed
Problem: A train travels 200 miles in 4 hours. At the same speed, how far can it travel in 10 hours?

Solution:
- Calculate the speed of the train:
\[
\text{Speed} = \frac{200 \text{ miles}}{4 \text{ hours}} = 50 \text{ miles per hour}
\]
- Distance traveled in 10 hours at the same speed:
\[
\text{Distance} = 50 \text{ miles per hour} \times 10 \text{ hours} = 500 \text{ miles}
\]

Answer: \( \boxed{500} \) miles.

---

#### 6. Candy Mix
Problem: A bag of candies contains a ratio of 3 red candies to 5 blue candies. If there are 18 red candies, how many blue candies are there?

Solution:
- The ratio of red to blue candies is \( 3:5 \).
- Let the number of blue candies be \( x \).
- Set up the proportion:
\[
\frac{3}{5} = \frac{18}{x}
\]
- Cross-multiply to solve for \( x \):
\[
3x = 18 \times 5
\]
\[
3x = 90
\]
\[
x = \frac{90}{3} = 30
\]

Answer: \( \boxed{30} \) blue candies.

---

#### 7. Dance Party
Problem: In a dance party, the ratio of boys to girls is 2:3. If there are 24 boys, how many girls are there?

Solution:
- The ratio of boys to girls is \( 2:3 \).
- Let the number of girls be \( x \).
- Set up the proportion:
\[
\frac{2}{3} = \frac{24}{x}
\]
- Cross-multiply to solve for \( x \):
\[
2x = 24 \times 3
\]
\[
2x = 72
\]
\[
x = \frac{72}{2} = 36
\]

Answer: \( \boxed{36} \) girls.

---

#### 8. Coin Collection
Problem: In a coin collection, the ratio of quarters to dimes is 5:2. If there are 15 quarters, how many dimes are there?

Solution:
- The ratio of quarters to dimes is \( 5:2 \).
- Let the number of dimes be \( x \).
- Set up the proportion:
\[
\frac{5}{2} = \frac{15}{x}
\]
- Cross-multiply to solve for \( x \):
\[
5x = 15 \times 2
\]
\[
5x = 30
\]
\[
x = \frac{30}{5} = 6
\]

Answer: \( \boxed{6} \) dimes.

---

#### 9. Coffee Mixing
Problem: A coffee blend consists of a ratio of 1 part dark roast to 4 parts medium roast. If you have 8 ounces of dark roast, how many ounces of medium roast should you use?

Solution:
- The ratio of dark roast to medium roast is \( 1:4 \).
- Let the amount of medium roast be \( x \) ounces.
- Set up the proportion:
\[
\frac{1}{4} = \frac{8}{x}
\]
- Cross-multiply to solve for \( x \):
\[
1x = 8 \times 4
\]
\[
x = 32
\]

Answer: \( \boxed{32} \) ounces of medium roast.

---

#### 10. Marathon Training
Problem: A runner can run 5 miles in 40 minutes. At the same speed, how long would it take to run 13.1 miles?

Solution:
- Calculate the speed of the runner:
\[
\text{Speed} = \frac{5 \text{ miles}}{40 \text{ minutes}} = 0.125 \text{ miles per minute}
\]
- Time to run 13.1 miles:
\[
\text{Time} = \frac{13.1 \text{ miles}}{0.125 \text{ miles per minute}} = 104.8 \text{ minutes}
\]

Answer: \( \boxed{104.8} \) minutes.

---

Final Answers:

1. \( \boxed{3} \)
2. \( \boxed{3.2} \)
3. \( \boxed{4} \)
4. \( \boxed{3.6} \)
5. \( \boxed{500} \)
6. \( \boxed{30} \)
7. \( \boxed{36} \)
8. \( \boxed{6} \)
9. \( \boxed{32} \)
10. \( \boxed{104.8} \)

Boxed Final Answer:
\[
\boxed{3, 3.2, 4, 3.6, 500, 30, 36, 6, 32, 104.8}
\]