Percentages Problems Worksheet 4 from MathCenter.org, featuring six word problems on calculating percentages.

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 know:
- 150 km = 75% of the total road length.
- Let the total road length be $ x $ km.

So,
$$
75\% \text{ of } x = 150 \\
\Rightarrow \frac{75}{100}x = 150 \\
\Rightarrow 0.75x = 150 \\
\Rightarrow x = \frac{150}{0.75} = 200
$$

✔ Answer: The road is 200 km long.

#### b. How many km are left?

Total road = 200 km
Already traveled = 150 km
Left = $ 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:

$$
0.35x = 17,500 \\
\Rightarrow x = \frac{17,500}{0.35} = 50,000
$$

✔ 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 original price be $ x $.
After 15% discount, it's sold at 85% of $ x $:

$$
0.85x = 63,750 \\
\Rightarrow x = \frac{63,750}{0.85} = 75,000
$$

✔ 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 10% increase, it becomes $ 1.10x $:

$$
1.10x = 9,500 \\
\Rightarrow x = \frac{9,500}{1.10} = 8,636.36 \ (\text{approx})
$$

✔ Answer: The price before 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% was removed, so 60% remains.

Remaining = $ 1\frac{1}{2} = 1.5 $ meters

Let original length be $ x $. Then:
$$
0.60x = 1.5 \\
\Rightarrow x = \frac{1.5}{0.60} = 2.5
$$

✔ 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 new price is:
$$
100\% + 250\% = 350\% \text{ of original}
$$
So, the price became 3.5 times the original.

But the question asks: "By what times was the price increased?"

This means: How many times more than original?
→ $ 3.5 - 1 = 2.5 $ times increased.

So, the price increased by 2.5 times (i.e., it became 2.5 times greater than original).

✔ Answer: The price increased by 2.5 times.

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

Let original price = $ x $

After 250% increase → new price = $ x + 2.5x = 3.5x $

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

✔ 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) 2.5 times
b) $5,000

Let me know if you'd like this formatted as a printable answer key!