# 6th Grade Math Word Problems (Percentages)

In this lesson, we will learn how to solve percent word problems

• using block diagrams or bar models or tape diagrams,
• using the grid method,
• using proportions.

### Using Bar Models

The following diagram shows an example of solving a percent word problem using bar models. Scroll down the page for more examples of how to solve percent word problems.

Example:
15% of the number of people who attended a concert arrived late. If 30 people arrived late, find the number of people who attended the concert.

Solution:

From the above model, we see that
15% → 30 people
1% → 30 ÷ 15 = 2 people
100% → 100 × 2 = 200 people
200 people attended the concert.

Examples of solving percent problems with bar models

Examples:

1. Marilyn saves 30% of the money she earns each month. She earns \$350 each month. How much does she save?

2. At the Natural History Museum, 40% of the visitors are children. There are 36 children at the museum. How many visitors altogether are at the museum?

3. Bill bought cards to celebrate Pi day. He sends 60% of his cards to friends. He sent 42 cards to friends. How many cards did he buy altogether?

4. Bruce cookies 80% of the pancakes at the pancake breakfast last weekend. They made 1120 pancakes. How many pancakes did Bruce cook?

The following video shows examples of finding total price with sales tax and an example of finding cost after discount using bar models.

Examples:

1. Alejandro bought a television set for \$900 and paid a sales tax of 8%. How much did he pay for the television set?

2. Alice saved for a new bike. The bike was on sale for a discount of 35%. The original cost of the bike was \$270. How much did she pay for the bike?

### Using Grid Method

Setting up the Percent Problem
Describes how to set up a percent problem using the grid method. Uses examples with the total given and looking for the parts.

Example:
There are 250 chairs in a room
a) If 150 chairs are full, what % are full?
b) What % are empty?

Multiple Step Percent Problems Part 1
Examples of how to solve percent word problems with the grid method.

Example 1: A stereo listed for \$350 is on sale for 20% off the list price. The sales tax is 6%. What price does a customer pay for the stereo if she buys it on sale?

Example 2: Stacey just received her annual cost-of-living raise. She previously earned \$1450 a month. Her new salary is \$1508. What is the rate of increase?

Example 3: At a playoff game, paid attendance was 39,900. The total attendance was 42,000. What percent of those attending had free tickets?

### Solving Percentage Word Problems Using Proportions

Practice solving percentage word problems by setting up a proportion and solving.

Example:
A poll was conducted by a local newspaper asking if the governor was doing a good job. 6,000 people were polled. If 2,400 said they approved of the job the governor was doing, what percent of the people polled disapproved?

Percent Word Problems: Percentage Problems
Shows how to solve “percent of” word problems using proportions.

Examples:

1. What is 15% of 40?
2. 12 is 20% of what number?
3. 22 is what percent of 5?
4. 4 is what percent of the quotient of 15 and 3?

Percent Word Problems: Sales and Discount
Solving percent word problems that involve finding a sale price given original price and discount, finding an original price given sale price and discount, and finding sale price given profit.

Example 1: A laptop that normally costs \$600 is offered at a discount of 35%. What is the new sale price?

Example 2: A pair of shoes is marked down 20% during a sale and costs \$60. What was the original price?

Percent Word Problems: Profit
Solving percent word problems that involve finding the percentage profit.

Example 1: The total cost of producing a tablet is \$150. If the manufacturer wants to make a 20% profit, at what price must they sell the tablet?

Example 2: Kevin bought a concert ticket for \$50 and sold it for \$54. What was the percentage profit?

Percent Word Problems: Percent Increase and Decrease
Solving percent word problems that involve percent increase and decrease.

Example 1: 15 fans attended a band’s first concert. 18 fans attended their second concert. What was the percent increase in the number of fans from the first concert to second?

Example 2: Last year, a football team won 15 games. This year, the team won 20% fewer games. How many games did the team win this year?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.