Solve percent equations: word problems
Key notes:
A percent is 1 part out of 100.
1% is equal to 1/100 or 0.01
Proportions can be used to solve percent problems.
part / whole = percent / 100
Learn with an example
➡️ The students in Emily’s grade voted to select a guest speaker. 20 students voted for a famous athlete. The other 80 students in Emily’s grade voted for a famous actor. What percentage of the students voted for the athlete?
Find the total number of students.
20 + 80 = 100
The part is 20.
The whole is 100.
Let n represent the percent.
Write a proportion to solve for n.
20 / 100 = n / 100
20 · 100 = 100n
2,000 = 100n
2,000 ÷ 100 = 100n ÷ 100
20 = n
20% of the students voted for the famous athlete.
You could also find the answer by writing and solving an equation:
part = percentage of whole
20 = n / 100 . 100
20 = 100n / 100
20 = n
20 ÷ 1 = n ÷ 1
20 = n
20% of the students voted for the famous athlete.
➡️ At the craft store, Duncan bought a bag of yellow and orange marbles. He received 39 yellow marbles and 13 orange marbles. What percentage of the marbles were yellow?
Find the total number of marbles.
39 + 13 = 52
The part is 39.
The whole is 52.
Let n represent the percent.
Write a proportion to solve for n.
39 / 52 = n / 100
39 · 100 = 52n
3,900 = 52n
3,900 ÷ 52 = 52n ÷ 52
75 = n
75% of the marbles were yellow.
You could also find the answer by writing and solving an equation:
part = percentage of whole
39 = n /100 . 52
39 = 52n / 100
39 = 0.52n
39 ÷ 0.52 = 0.52n ÷ 0.52
75 = n
75% of the marbles were yellow.
➡️ This morning, Elise took a history test. She got 3 out of 4 problems right. What percentage did Elise get right?
Find what percentage 3 is of 4. The part is 3.
The whole is 4.
Let n represent the percent.
Write a proportion to solve for n.
3 / 4 = n /100
3 · 100 = 4n
300 = 4n
300 ÷ 4 = 4n ÷ 4
75 = n
3 · 100 = 4n
300 = 4n
300 ÷ 4 = 4n ÷ 4
75 = n
Elise got 75% of the questions right.
You could also find the answer by writing and solving an equation:
part = percentage of whole
3 = n / 100 . 4
3 = 4n / 100
3 = 0.04n
3 ÷ 0.04 = 0.04n ÷ 0.04
75 = n
Elise got 75% of the questions right.
Let’s practice! 🖊️
