Math worksheet on percent word problems using decimal expressions, featuring 10 questions with answer spaces.

Problem: Solve the given percent word problems and determine the correct expressions for each scenario.

#### 1. A cell phone company dropped the prices on their phones by 9%. Which expression shows the new price of the phone (p)?
- Options:
- A. \( p - 0.09p \)
- B. \( p \times 1.09 \)
- C. \( p \times 0.09 \)
- D. \( p - 0.09 \)

Solution:
If the price of the phone is reduced by 9%, the new price is calculated as:
\[ \text{New Price} = \text{Original Price} - (\text{Original Price} \times 0.09) \]
\[ \text{New Price} = p - 0.09p \]

Correct Answer: A. \( p - 0.09p \)

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#### 2. Over the summer gas prices dropped 3%. Which expression shows the new price of a gallon of gas (the old price is represented by \( g \))?
- Options:
- A. \( g \times 0.03 \)
- B. \( g - 0.03 \)
- C. \( g \times 0.97 \)
- D. \( g - 0.03g \)

Solution:
If gas prices drop by 3%, the new price is:
\[ \text{New Price} = \text{Original Price} - (\text{Original Price} \times 0.03) \]
\[ \text{New Price} = g - 0.03g \]
Alternatively, this can be expressed as:
\[ \text{New Price} = g \times (1 - 0.03) = g \times 0.97 \]

Correct Answer: C. \( g \times 0.97 \)

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#### 3. While clearing out some old inventory a store offered 10 percent off of any item (i). Which expression can be used to calculate the new cost of an item?
- Options:
- A. \( i - 1.1 \)
- B. \( i - 0.1i \)
- C. \( i \times 0.1 \)
- D. \( i - 0.1 \)

Solution:
If the store offers a 10% discount, the new cost of the item is:
\[ \text{New Cost} = \text{Original Cost} - (\text{Original Cost} \times 0.1) \]
\[ \text{New Cost} = i - 0.1i \]

Correct Answer: B. \( i - 0.1i \)

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#### 4. Joe was earning $11 an hour before his raise. After his 5% raise he is making $11.55 an hour. Which expression shows how his new hourly rate was calculated?
- Options:
- A. \( 11 \times 1.05 \)
- B. \( 11 \times 0.05 \)
- C. \( 11 + 0.05 \)
- D. \( 11 + 0.05 \)

Solution:
If Joe received a 5% raise, his new hourly rate is:
\[ \text{New Hourly Rate} = \text{Original Hourly Rate} + (\text{Original Hourly Rate} \times 0.05) \]
\[ \text{New Hourly Rate} = 11 + (11 \times 0.05) \]
This can also be expressed as:
\[ \text{New Hourly Rate} = 11 \times (1 + 0.05) = 11 \times 1.05 \]

Correct Answer: A. \( 11 \times 1.05 \)

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#### 5. A mall kiosk needed to buy 33 new cell phone cases at \( z \) dollars a piece. Because they were buying so many they got 5% off the price. Which expression shows how much they saved?
- Options:
- A. \( 33z \times 0.05 \)
- B. \( 0.05 \times 33z \)
- C. \( 33z \times 0.05 \)
- D. \( 33z + 0.05 \)

Solution:
The total cost without the discount is \( 33z \). With a 5% discount, the amount saved is:
\[ \text{Amount Saved} = \text{Total Cost} \times 0.05 \]
\[ \text{Amount Saved} = 33z \times 0.05 \]

Correct Answer: A. \( 33z \times 0.05 \)

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#### 6. Roger drew a square with each side being exactly 12 centimeters long. If he wanted to make the square 6% larger, which expression can he use to find the new side lengths?
- Options:
- A. \( 12 \times 1.06 \)
- B. \( 12 \times 1.06 \)
- C. \( 12 \times 0.06 \)
- D. \( 12 + 0.06 \)

Solution:
To increase the side length by 6%, the new side length is:
\[ \text{New Side Length} = \text{Original Side Length} \times (1 + 0.06) \]
\[ \text{New Side Length} = 12 \times 1.06 \]

Correct Answer: A. \( 12 \times 1.06 \)

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#### 7. The regular price of a computer was $893, but over the weekend it'll be on sale for 10 percent off. Which expression shows the difference in price from normal to sale?
- Options:
- A. \( n - 10 \)
- B. \( n \times 0.1 \)
- C. \( n - 1.1 \)
- D. \( n - 0.1 \)

Solution:
If the computer is on sale for 10% off, the discount amount is:
\[ \text{Discount Amount} = \text{Regular Price} \times 0.1 \]
\[ \text{Discount Amount} = n \times 0.1 \]

Correct Answer: B. \( n \times 0.1 \)

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#### 8. A house was on sell for $23,474. If you wanted to offer 7% less than the asking price (\( p \)), which expression shows how much you should offer?
- Options:
- A. \( p - 0.07 \)
- B. \( p - 0.07p \)
- C. \( p - 1.07 \)
- D. \( p \times 0.07 \)

Solution:
If you want to offer 7% less than the asking price, your offer is:
\[ \text{Offer} = \text{Asking Price} - (\text{Asking Price} \times 0.07) \]
\[ \text{Offer} = p - 0.07p \]

Correct Answer: B. \( p - 0.07p \)

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#### 9. A company was having a sale for 19% off the price of computer monitors. Which expression shows how much money you would save if you bought 25 monitors for \( z \) dollars a piece?
- Options:
- A. \( 25z \times 0.19 \)
- B. \( 25z \times 1.19 \)
- C. \( 0.19 \times 25z \)
- D. \( 25z + 0.19 \)

Solution:
The total cost without the discount is \( 25z \). With a 19% discount, the amount saved is:
\[ \text{Amount Saved} = \text{Total Cost} \times 0.19 \]
\[ \text{Amount Saved} = 25z \times 0.19 \]

Correct Answer: A. \( 25z \times 0.19 \)

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#### 10. Last year the price of a college textbook (\( b \)) was $197. This year the price will be 13% higher. Which expression shows the difference in price from last year to this year?
- Options:
- A. \( b \times 0.13 \)
- B. \( b - 1.13 \)
- C. \( b - 0.13 \)
- D. \( b - 13 \)

Solution:
If the price increases by 13%, the increase in price is:
\[ \text{Price Increase} = \text{Last Year's Price} \times 0.13 \]
\[ \text{Price Increase} = b \times 0.13 \]

Correct Answer: A. \( b \times 0.13 \)

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Final Answers:

1. A. \( p - 0.09p \)
2. C. \( g \times 0.97 \)
3. B. \( i - 0.1i \)
4. A. \( 11 \times 1.05 \)
5. A. \( 33z \times 0.05 \)
6. A. \( 12 \times 1.06 \)
7. B. \( n \times 0.1 \)
8. B. \( p - 0.07p \)
9. A. \( 25z \times 0.19 \)
10. A. \( b \times 0.13 \)

Boxed Final Answer:
\[
\boxed{
\begin{array}{ll}
1. & \text{A. } p - 0.09p \\
2. & \text{C. } g \times 0.97 \\
3. & \text{B. } i - 0.1i \\
4. & \text{A. } 11 \times 1.05 \\
5. & \text{A. } 33z \times 0.05 \\
6. & \text{A. } 12 \times 1.06 \\
7. & \text{B. } n \times 0.1 \\
8. & \text{B. } p - 0.07p \\
9. & \text{A. } 25z \times 0.19 \\
10. & \text{A. } b \times 0.13 \\
\end{array}
}
\]