### Key Concepts

- Percent equation.
- Find the percent.
- Find the part.
- Find the whole.

**3.3 Represent and use the percent equation**

**What is percent equation?**

The percent equation is a constant of proportionality that relates a part to the whole. The equation has the same form as Distance = Speed×time.

**Deducing the percent equation:**

part / whole =p/100

part/whole =percent

part / whole × whole = percent × whole

Part = percent × whole

Therefore, percent equation can be written as Part = percent × whole.

**Example 1: **In a math class, students compared their vertical reach against their heights. Mary is 50 inches tall and can reach 75 inches. What percent of her total vertical reach is her height?

**Solution: **We know that, Part = percent × whole

Here we understand that, part = height of Mary and Whole = vertical reach of Mary.

Let us take percent as **p**, which we are about to find.

50 = **p** × 75

Divide the equation by 75 on both the sides.

50/75=p ×75 / 75

50/75 = p

p = 0.67

Multiply by 100 and add the percent symbol.

p = 67%

Therefore, Mary’s height is 67% of her vertical reach.

**3.3.1 Find the percent**

**Example 1: **A Rhinoceros weighs 10000 pounds on earth and 2000 pounds on the Moon. What percent of its weight on moon is its weight on the earth?

**Solution: **We know that, Part = percent × whole

Here we understand that, part = weight on moon and Whole = weight on the earth.

Let us take percent as p, which we are about to find.

2000 = p × 10000

Divide the equation by 10000 on both the sides.

2000 / 10000 = p ×10000 / 10000

2000 / 10000 = p

p = 0.2

Multiply by 100 on both sides and add the percent symbol.

P/100× 100 = 0.2 × 100 [ p here is percent i.e.,P/100]

P = 20%

Therefore, weight of rhinoceros on moon is 20% of its weight on the earth.

**Example 2: **Drake scores 10 out of 25 goals in a match. What is the striking percent of Drake of the total goals scored in the match?

**Solution: **We know that, Part = percent × whole

Here we understand that, part = goals scored by Drake and Whole = Total goals scored in the match.

Let us take percent as p, which we are about to find.

10 = p × 25

Divide the equation by 25 on both the sides.

10/25 =p ×25 / 25

10/25 =p

p = 0.4

Multiply by 100 on both sides and add the percent symbol.

P/100× 100 = 0.4 × 100 [ p here is percent i.e.,P/100]

P = 40%

Therefore, striking percent of Drake is 40% of the total goals scored in that match.

**3.3.2 Find the part**

**Example 1: **A school collects 20% of the total fee as donation. If the total fee per student is $10000 per year. What is the donation collect per student?

**Solution: **We know that, Part = percent × whole

Here we understand that, **p **= percent of donation and Whole = Total fee per annum.

Let us take part as **x**, which we are about to find.

**x** = 20% × 10000

**x** = 20 /100× 10000

Express the percent as the decimal

**x** = 0.2 × 10000

x= 2000

The value of the part is found to be 2000.

Therefore, we conclude that school collects a donation of $2000 per student.

**Example 2: **In USA, it is a universal rule that a tip of 15% of the bill amount must be given to the waiters.

A family dines at a restaurant and pays $680. How much tip should be given to the waiter?

**Solution: **We know that, Part = percent × whole

Here we understand that, p = percent of tip and Whole = Bill paid.

Let us take part as **x**, which we are about to find.

**x **= 15% × 680

**x** =15/100× 680

Express the percent as the decimal

**x** = 0.15 × 680

x=102

The value of the part is found to be 102.

Therefore, we conclude that waiter gets $102.

**3.2.3 Find the whole**

**Example 1: **Cathy earns 2.15% commission on selling an insurance policy per customer. If she earned $430 in commission. What is the premium amount of the policy?

**Solution: **We know that, Part = percent × whole

Here we understand that, **p** = percent of commission and Part = commission earned per customer.

Let us take whole as w, which we are about to find.

430 = 2.15% × **w**

Express the percent as the decimal

430 = 0.0215 × **w**

Divide by 0.0215 on both sides of the equation

430 / 0.0215=

0.0215 / 0.0215 × **w**

430 / 0.0215 = **w**

**w** = 20000

The value of the whole is found to be 20000.

Therefore, we conclude that premium of the policy sold is $20000.

**Example 2: **The local newspaper has 40 letters addressed to its editor, if this represents 5% of all the newspaper’s readers. How many readers does the newspaper have?

**Solution: **We know that, Part = percent × whole

Here we understand that, **p **= percent of newspaper readers and Part = Number of letters received of all the readers.

Let us take whole as **w**, which we are about to find.

40 = 5% × **w**

Express the percent as the decimal

40 = 0.05 × **w**

Divide by 0.05 on both sides of the equation

40 / 0.05 = 0.05/ 0.05 × **w**

40 / 0.05= **w**

**w** = 800

The value of the whole is found to be 800.

## Exercise:

- In a class of 50 students, 11 of them are left-handed. What percent of left-handed students are there in the total class?
- What percent is 125 out of 900?
- A group of 20 people planned for a vacation. 12 of them wanted to go to Africa, whereas the others wanted to tour India. Find which country has greater percent of the total people who wish to visit it.
- An auto insurance company pays 13% commission to its agents for each new insurance policy they sell. How much commission does an agent make on $5000 policy?
- Lara pays 15% of her income on mutual funds, if she earns $12000 per month, what amount is invested by her in stocks?
- A restaurant charges a 20% gratuity if a party has 5 or more people. How much gratuity is added to a party of 7 on $150 bill?
- In a company 40% of the workers are men. If, 1200 men work for the company, how many workers are there in all?
- Hedge makes 3% commission on each jewelry he sells. Last week he earned $100 in commission on one such piece. How much did the jewelry cost the client?
- In a library 2600 books are a work of fiction, which makes 35 % of the total books. Determine the total number of books in the library.
- A shirt that normally costs $35 is on sale for $20. What percent of the regular price is the sales price?

### What have we learned?

- Understanding and deducing the percent equation.
- Finding the percent.
- Finding the part.
- Finding the whole.

### Mind Map

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