Easy Way To Solve Percent Equation

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:

1. In a class of 50 students, 11 of them are left-handed. What percent of left-handed students are there in the total class?
2. What percent is 125 out of 900?
3. 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.
4. 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?
5. Lara pays 15% of her income on mutual funds, if she earns $12000 per month, what amount is invested by her in stocks?
6. 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?
7. In a company 40% of the workers are men. If, 1200 men work for the company, how many workers are there in all?
8. 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?
9. 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.
10. 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