Quiz worksheet on algebraic expressions with multiple-choice questions.

Problem Analysis:

The task involves translating word phrases into algebraic expressions and interpreting a table to derive a rule for the total cost of renting a scooter. Let's solve each part step by step.

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Question 1:

Word Phrase: The quotient of a number and seven
Solution:
- The quotient means division.
- A number can be represented as \( n \).
- Dividing a number by seven is written as \( \frac{n}{7} \).

Correct Answer: D. \( \frac{n}{7} \)

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Question 2:

Word Phrase: 74 less than a number
Solution:
- "Less than" indicates subtraction.
- A number can be represented as \( n \).
- Subtracting 74 from a number is written as \( n - 74 \).

Correct Answer: A. \( n - 74 \)

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Question 3:

Word Phrase: Five times a number
Solution:
- "Five times" indicates multiplication by 5.
- A number can be represented as \( n \).
- Multiplying a number by 5 is written as \( 5n \).

Correct Answer: C. \( 5n \)

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Question 4:

Word Phrase: 4 more than twice a number \( x \)
Solution:
- "Twice a number \( x \)" means \( 2x \).
- "4 more than" indicates addition of 4.
- Adding 4 to \( 2x \) is written as \( 2x + 4 \).

Correct Answer: B. \( 2(x + 4) \)

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Question 5:

Word Phrase: The product of 9 and the sum of a number \( x \) and 2
Solution:
- "The sum of a number \( x \) and 2" is \( x + 2 \).
- "The product of 9 and" indicates multiplication by 9.
- Multiplying 9 by \( x + 2 \) is written as \( 9(x + 2) \).

Correct Answer: A. \( 9(x + 2) \)

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Question 6:

Task: The table shows how the cost of renting a scooter depends on how long it is rented. What is a rule for the total cost? Give the rule in words and as an algebraic expression.

#### Table Data:
| Hours | Cost |
|-------|------|
| 1 | $17.50 |
| 2 | $35.00 |
| 3 | $52.50 |

Solution:
1. Identify the Pattern:
- For 1 hour, the cost is $17.50.
- For 2 hours, the cost is $35.00, which is \( 2 \times 17.50 \).
- For 3 hours, the cost is $52.50, which is \( 3 \times 17.50 \).

2. Determine the Rule:
- The cost increases linearly with the number of hours.
- The cost per hour is $17.50.
- If \( h \) represents the number of hours, the total cost \( C \) is given by:
\[
C = 17.50 \times h
\]

3. Express the Rule in Words:
- The total cost is $17.50 multiplied by the number of hours rented.

Final Answer:
- In Words: The total cost is $17.50 times the number of hours rented.
- Algebraic Expression: \( C = 17.50h \)

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Final Answers:

1. D. \( \frac{n}{7} \)
2. A. \( n - 74 \)
3. C. \( 5n \)
4. B. \( 2(x + 4) \)
5. A. \( 9(x + 2) \)
6. In Words: The total cost is $17.50 times the number of hours rented.
Algebraic Expression: \( C = 17.50h \)

Boxed Final Answer for Question 6:
\[
\boxed{C = 17.50h}
\]