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

Let's solve each problem step by step from the Percentages Problems Worksheet 4.

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1. A car rides 150 km, which is 75% of the road.

#### a. How long is the road?
We are told that 150 km = 75% of the total road length.

Let the total length of the road be $ x $ km.

So:
$$
75\% \text{ of } x = 150 \\
0.75x = 150
$$

Now divide both sides by 0.75:
$$
x = \frac{150}{0.75} = 200
$$

✔ Answer: The road is 200 km long.

#### b. How many km are left?
Total road = 200 km
Already traveled = 150 km
Remaining = $ 200 - 150 = 50 $ km

✔ Answer: 50 km are left.

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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?

Let the original price be $ x $.
It was sold for 35% of $ x $, so:
$$
0.35x = 17,500
$$

Solve for $ x $:
$$
x = \frac{17,500}{0.35} = 50,000
$$

✔ Answer: The original price was $50,000.

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3. A car was sold for $63,750 after a discount of 15%.

#### a. What was the price before discount?

Let the original price be $ x $.
After a 15% discount, the selling price is 85% of $ x $:
$$
0.85x = 63,750
$$

Solve for $ x $:
$$
x = \frac{63,750}{0.85} \approx 75,000
$$

✔ Answer: The price before discount was $75,000.

#### b. What was the discount amount?

Discount = Original price - Selling price
$$
= 75,000 - 63,750 = 11,250
$$

Alternatively:
15% of $75,000 = $0.15 × 75,000 = $11,250

✔ Answer: The discount amount was $11,250.

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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?

Let original price be $ x $.
After a 10% increase, new price = $ 1.10x $

$$
1.10x = 9,500
$$

$$
x = \frac{9,500}{1.10} \approx 8,636.36
$$

✔ Answer: The price before the increase was approximately $8,636.36.

#### b. How much did the price raise?

Increase = $ 9,500 - 8,636.36 = 863.64 $

Or: 10% of $8,636.36 = $863.64

✔ Answer: The price increased by $863.64.

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5. A rope was cut short by 0.4 of its length, and the remaining rope is $ 1\frac{1}{2} $ meters long. What was the original length?

"Cut short by 0.4" means 40% of the rope was removed, so 60% remains.

Let original length be $ x $ meters.

Then:
$$
0.6x = 1\frac{1}{2} = 1.5
$$

$$
x = \frac{1.5}{0.6} = 2.5
$$

✔ Answer: The original length was 2.5 meters.

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6. A product price was raised by 250%.

#### a. By what times was the price increased?

A 250% increase means the price becomes:
$$
100\% + 250\% = 350\% \text{ of original}
$$

So, the new price is $ 3.5 $ times the original.

✔ Answer: The price was increased by 3.5 times.

#### b. What was the original price if the current price is $17,500?

Let original price be $ x $.
After 250% increase:
$$
3.5x = 17,500
$$

$$
x = \frac{17,500}{3.5} = 5,000
$$

✔ Answer: The original price was $5,000.

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✔ Final Answers Summary:

1. a. 200 km
b. 50 km

2. $50,000

3. a. $75,000
b. $11,250

4. a. $8,636.36
b. $863.64

5. 2.5 meters

6. a. 3.5 times
b. $5,000

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