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Word Problems That Require Equations or Inequalities

HSA-CED.A.3
Answer Keys Here

Aligned To Common Core Standard:

High School - HSA-CED.A.3

How to Write a System of Equations - When you are solving real-world algebraic equations, you can get easily confused. Considering that such problems are complex to solve and are known as the system of equations. Let us consider an example to learn its concept quickly. David spent $131 one pair of shoes, since one pair of sneakers had a price of $15, while the slippers had a cost of $28. In total, he bought 7 pairs of shoes. How many pairs of each shoe did he buy of each type? In this section, we are only learning how to write the system of equations and not solve them. In this problem, we have to write two equations, given that there are two variables. The two variables are the two pairs of shoes, i.e., the sneakers and the slippers. Let us consider the two variables like x and y. Now, in total, David bought 7 pairs of shoes comprising of the two variables. So, the first equation becomes: [1] => x+y=7 The first equation depicts the number of shoes bought by David. The second equation will illustrate the total money he spent. He spent a total of $131 comprising of $15 worth of x’s and $28 worth of y’s. So, the equation becomes: [2] => 15x+28y=7 Now, you have two equations that you need to simultaneously solve to find out how many pairs did David bought for each type of shoes. These worksheets and lessons teach students how to write equations and inequalities that are based on word problems.

Printable Worksheets And Lessons






Homework Sheets

This section took me forever to write. I just kept running out of ideas.

  • Homework 1 - Jian wants to take part in a Taekwondo class. He has two choices. Taekwondo class A costs $10 per month and $100 as registration fees.
  • Homework 2 - Wilson is planning to open a Yoga studio. He has to pay $30 as rent for the studio and $5 per member for utilities. Each member will pay $15 for the yoga class.
  • Homework 3 - George makes an average 15 baskets per game and made 40 baskets so far. Shane makes an average 10 baskets per game and made 55 baskets so far. If their averages remain the same, how many games do they have to play in order to score the same number of baskets?



Practice Worksheets

A big thanks to all my past colleagues that throw ideas at me to come up with new problems on this one.

  • Practice 1 - Daniel has an office. He has to pay $20 a day in rent for the office and $2 per hour for parking. He pays $30 each day. How many hours does Daniel park his car?
  • Practice 2 - Emma organized a party in a club. She has to pay $200 to an event organizer and her expenses for dinner are $10 per person. Each person pays $15 to Emma. How many people does Emma need to come to the party to reach a breakeven point?
  • Practice 3 - Eva wants to print copies of her notes in hardcover book format. She has two choices. Printing A costs a setup fee of $40 and $3 for every book. Printing B costs a setup fee of $30 and $4 for every book. Find out when the two options cost the same amount. How many books is that?



Math Skill Quizzes

This can be a challenging task for many students.

  • Quiz 1 - Two road crews are paving a straight section of road. The first crew has completed paving 12 miles and is completing 2 additional miles per day. The second crew has finished 8 miles and is completing 3 miles per day. How long will it take for both teams to cover the same number of miles?
  • Quiz 2 - Vijay was renting a skateboard for his competition training. Skateboard A is $12 per month and requires a down payment of $100. Skateboard B is $15 per month rent and requires a down payment of $80. How many months would Vijay need to rent the skateboard in order for the total cost to be same?
  • Quiz 3 - Marlin and Watson are playing video games. Marlin has 40 points and is earning 5 points every turn. Watson has 50 points and is earning 3 points every turn. In a certain number of turns, the score will be tied. How many points will they each have?