2. On a map, each centimeter represents 45 kilometers. Two towns are 135 kilometers apart. What is the distance between the towns on the map? The towns are centimeters apart on the map. 3. A certain recipe calls for 2 cups of flour and 3 ounces of oil. If the recipe is increased to use 8 cups of flour, how much oil should be used? 4. An 8 -inch by 12 -inch portrait is reduced to be "pocket size." If the shorter side is now 2 inches, how long is the longer side? The longer side is 5. Tim practices guitar 3 hours for every I hour he plays basketball. He practiced guitar 244 hours last month. How many hours did he play basketball? Tim played basketball _ 6. The shipping charge on a 30 -pound package is $$ \$ 6 $$. How much would the shipping cost be on a 50 -pound package? The shipping cost would be 7. A new school has a teacher-to-student ratio of $$ 2: 15 $$. The school has 42 teachers. How many students are there in the school? There are of should be used.

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**2. Map Distance Problem**

- Each centimeter represents $$45$$ kilometers.
- The actual distance between the towns is $$135$$ kilometers.
- The distance on the map is  
  $$
  \frac{135}{45} = 3 \text{ centimeters}.
  $$
  
**3. Recipe Adjustment Problem**

- The original recipe uses $$2$$ cups of flour and $$3$$ ounces of oil.
- The ratio of oil to flour is  
  $$
  \frac{3 \text{ ounces}}{2 \text{ cups}}.
  $$
- When the recipe uses $$8$$ cups of flour, the amount of oil needed is  
  $$
  8 \times \frac{3}{2} = 12 \text{ ounces}.
  $$

**4. Portrait Scaling Problem**

- The original portrait dimensions are $$8$$ inches by $$12$$ inches (with the shorter side being $$8$$ inches).
- The reduction sets the shorter side to $$2$$ inches.
- The scale factor is  
  $$
  \frac{2}{8} = \frac{1}{4}.
  $$
- The longer side is reduced to  
  $$
  12 \times \frac{1}{4} = 3 \text{ inches}.
  $$

**5. Tim’s Practice Problem**

- Tim practices guitar $$3$$ hours for every $$1$$ hour of basketball. Hence, the ratio for guitar to basketball is $$3:1$$.
- Let $$x$$ be the hours spent playing basketball.
- Given that guitar practice was $$244$$ hours, we have  
  $$
  3x = 244.
  $$
- Solving for $$x$$:  
  $$
  x = \frac{244}{3} \text{ hours}.
  $$

**6. Shipping Cost Problem**

- A $$30$$-pound package costs $$\$6$$, so the cost per pound is  
  $$
  \frac{6}{30} = 0.20 \text{ dollars per pound}.
  $$
- For a $$50$$-pound package, the shipping cost is  
  $$
  50 \times 0.20 = 10 \text{ dollars}.
  $$

**7. Teacher-to-Student Ratio Problem**

- The ratio of teachers to students is $$2:15$$.
- With $$42$$ teachers, let the number of students be $$S$$.
- Using the ratio, we have  
  $$
  \frac{S}{42} = \frac{15}{2}.
  $$
- Solving for $$S$$:  
  $$
  S = 42 \times \frac{15}{2} = 42 \times 7.5 = 315.
  $$
  
Thus, the answers are:

2. $$3$$ centimeters  
3. $$12$$ ounces of oil  
4. $$3$$ inches  
5. $$\frac{244}{3}$$ hours  
6. $$\$10$$  
7. $$315$$ students
2. 3 centimeters 3. 12 ounces of oil 4. 3 inches 5. 244⁄3 hours 6. \$10 7. 315 students

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