Percentage Problems Worksheet 4 | Worksheets | Math Center - Free Printable

Let's solve each problem step by step.

---

Problem 1:

A car rides 150 km, which is 75% of the road.
a. How long is the road?
b. How many km are left?

#### Solution:
- Let the total length of the road be \( x \) km.
- According to the problem, 150 km is 75% of the road:
\[
150 = 0.75x
\]
- Solve for \( x \):
\[
x = \frac{150}{0.75} = 200 \text{ km}
\]

- The total length of the road is \( 200 \) km.

- To find how many km are left:
\[
\text{Remaining distance} = \text{Total distance} - \text{Distance traveled}
\]
\[
\text{Remaining distance} = 200 - 150 = 50 \text{ km}
\]

#### Final Answers:
a. The total length of the road is \( \boxed{200} \) km.
b. The remaining distance is \( \boxed{50} \) km.

---

Problem 2:

Damaged goods are sold for 35% of its price. What would be the original price of the goods if it was sold for $17,500?

#### Solution:
- Let the original price of the goods be \( P \).
- According to the problem, the goods were sold for 35% of the original price:
\[
0.35P = 17,500
\]
- Solve for \( P \):
\[
P = \frac{17,500}{0.35} = 50,000
\]

#### Final Answer:
The original price of the goods is \( \boxed{50,000} \).

---

Problem 3:

A car was sold for $63,750 after a discount of 15%.
a. What was the price before discount?
b. What was the discount amount?

#### Solution:
- Let the original price of the car be \( P \).
- After a 15% discount, the car was sold for 85% of its original price:
\[
0.85P = 63,750
\]
- Solve for \( P \):
\[
P = \frac{63,750}{0.85} = 75,000
\]

- The original price of the car is \( 75,000 \).

- To find the discount amount:
\[
\text{Discount amount} = \text{Original price} - \text{Selling price}
\]
\[
\text{Discount amount} = 75,000 - 63,750 = 11,250
\]

#### Final Answers:
a. The original price before discount is \( \boxed{75,000} \).
b. The discount amount is \( \boxed{11,250} \).

---

Problem 4:

The price of a piece of furniture was raised by 10% and it was sold for $9500.
a. What was the price before the increase?
b. How much did the price raise?

#### Solution:
- Let the original price of the furniture be \( P \).
- After a 10% increase, the price became 110% of the original price:
\[
1.10P = 9500
\]
- Solve for \( P \):
\[
P = \frac{9500}{1.10} = 8636.36 \text{ (approximately)}
\]

- The original price of the furniture is \( 8636.36 \).

- To find the price increase:
\[
\text{Price increase} = \text{New price} - \text{Original price}
\]
\[
\text{Price increase} = 9500 - 8636.36 = 863.64 \text{ (approximately)}
\]

#### Final Answers:
a. The original price before the increase is \( \boxed{8636.36} \).
b. The price increase is \( \boxed{863.64} \).

---

Problem 5:

A rope was cut short by 0.4 of its length, and the remaining rope is 1.2 meters long. What was the original length?

#### Solution:
- Let the original length of the rope be \( L \).
- After cutting off 0.4 of its length, the remaining length is 60% of the original length:
\[
0.6L = 1.2
\]
- Solve for \( L \):
\[
L = \frac{1.2}{0.6} = 2
\]

#### Final Answer:
The original length of the rope is \( \boxed{2} \) meters.

---

Problem 6:

A product price was raised by 250%.
a. By what times was the price increased?
b. What was the original price if the current price is $17,500?

#### Solution:
- A 250% increase means the price becomes 350% of the original price (since \( 100\% + 250\% = 350\% \)).

#### Part (a):
- The price was increased by a factor of:
\[
3.5 \text{ times}
\]

#### Part (b):
- Let the original price be \( P \).
- After a 250% increase, the new price is 350% of the original price:
\[
3.5P = 17,500
\]
- Solve for \( P \):
\[
P = \frac{17,500}{3.5} = 5,000
\]

#### Final Answers:
a. The price was increased by \( \boxed{3.5} \) times.
b. The original price is \( \boxed{5,000} \).

---

Final Summary of All Answers:

1. a. \( \boxed{200} \) km, b. \( \boxed{50} \) km
2. \( \boxed{50,000} \)
3. a. \( \boxed{75,000} \), b. \( \boxed{11,250} \)
4. a. \( \boxed{8636.36} \), b. \( \boxed{863.64} \)
5. \( \boxed{2} \) meters
6. a. \( \boxed{3.5} \), b. \( \boxed{5,000} \)