Question

A recipe calls for 34 cup of sugar. If you want to make 1 12 times the recipe, you’ll need ____ cups of sugar.
2. The temperature dropped 2 14 degrees every hour for 6 hours. The total temperature change was ____ degrees.
3. A car travels at a speed of 55 12 miles per hour for 2 34 hours. The total distance traveled is ____ miles.
4. A bakery uses 23 of a pound of butter for each batch of cookies. If they make 5 batches, they’ll use ____ pounds
of butter.
5. A piece of fabric is 4 14 yards long. If it’s cut into pieces that are each 34 yard long, there will be ____ pieces.
6. The depth of a swimming pool increases by 18 foot every 3 feet of length. If the pool is 36 feet long, the total
depth increase from one end to the other is ____ feet.
7. A company’s stock price decreased by 16 of its value each month for 3 months. If the original price was $60, what
was the final stock price?

Answer 1

Let's solve each of these problems step by step:

1. **Sugar Calculation**
- The recipe calls for \( \frac{3}{4} \) cup of sugar.
- To make \( 1 \frac{1}{2} \) times the recipe, we first express \( 1 \frac{1}{2} \) as \( \frac{3}{2} \).
- Calculate the needed amount of sugar:
\[
\frac{3}{2} \times \frac{3}{4} = \frac{9}{8} \text{ cups.}
\]
- This can be written as \( 1 \frac{1}{8} \) cups of sugar.

2. **Temperature Change Calculation**
- The temperature dropped \( 2 \frac{1}{4} \) degrees every hour for 6 hours.
- First, express \( 2 \frac{1}{4} \) as \( \frac{9}{4} \).
- Total temperature change:
\[
6 \times \frac{9}{4} = \frac{54}{4} = 13 \frac{1}{2} \text{ degrees.}
\]

3. **Distance Calculation**
- The car travels at \( 55 \frac{1}{2} \) miles per hour for \( 2 \frac{3}{4} \) hours.
- Express \( 55 \frac{1}{2} \) as \( \frac{111}{2} \) and \( 2 \frac{3}{4} \) as \( \frac{11}{4} \).
- Total distance:
\[
\frac{111}{2} \times \frac{11}{4} = \frac{1221}{8} \text{ miles.}
\]
- This can be simplified to \( 152 \frac{5}{8} \) miles.

4. **Butter Calculation**
- The bakery uses \( \frac{2}{3} \) of a pound of butter for each batch.
- If they make 5 batches:
\[
5 \times \frac{2}{3} = \frac{10}{3} \text{ pounds.}
\]
- This is \( 3 \frac{1}{3} \) pounds of butter.

5. **Fabric Pieces Calculation**
- The fabric is \( 4 \frac{1}{4} \) yards long, which can be written as \( \frac{17}{4} \) yards.
- Each piece is \( \frac{3}{4} \) yards long.
- Number of pieces:
\[
\frac{17}{4} \div \frac{3}{4} = \frac{17}{4} \times \frac{4}{3} = \frac{17}{3} \approx 5.67 \text{ pieces.}
\]
- Therefore, there are 5 full pieces.

6. **Pool Depth Calculation**
- The depth increases by \( \frac{1}{8} \) foot every 3 feet of length.
- For a pool that is 36 feet long:
\[
\frac{36}{3} \times \frac{1}{8} = 12 \times \frac{1}{8} = \frac{12}{8} = \frac{3}{2} \text{ feet, or } 1.5 \text{ feet.}
\]

7. **Stock Price Calculation**
- The stock price decreased by \( \frac{1}{6} \) of its value each month for 3 months.
- The value decrease per month is \( \frac{1}{6} \) of $60:
\[
\frac{1}{6} \times 60 = 10.
\]
- Total decrease over 3 months:
\[
3 \times 10 = 30.
\]
- Final stock price:
\[
60 - 30 = 30 \text{ dollars.}
\]

To summarize the answers:
1. \( 1 \frac{1}{8} \) cups of sugar.
2. \( 13 \frac{1}{2} \) degrees.
3. \( 152 \frac{5}{8} \) miles.
4. \( 3 \frac{1}{3} \) pounds of butter.
5. 5 pieces.
6. \( 1.5 \) feet.
7. $30.