Writing Equations From Word Problems Worksheets
Up to this point when we have working with word problems, they have been pretty straight forward and require a step or two. Now that we have learned the anatomy of equations, we can use them to model more complex situations and scenarios that these problems may throw our way. This is a powerful skill to learn. This are the types of questions you will be trying to answer for yourself on a daily basis. Once you have mastered them, you will have a much greater understanding of your environment and how to make good decisions. These worksheets will help you learn the process of putting everything together for yourself.
Aligned Standard: Grade 7 Expression & Equations - 7.EE.B.4a
- Michael's Plate Dilemma Step-by-step Lesson- We break apart a recent purchase that Michael made to figure out unit cost.
- Guided Lesson - Solve for x as a refresher. Then we focus on some unit costs and cost breakdown. Equations help a bunch here. You just need to follow through with them.
- Guided Lesson Explanation - I tried everything to keep it to one page, but it didn't work out.
- Practice Worksheet - The word problems are super random. What do water melons, antiques, and socks have to do with one another?
- Matching Worksheet - Gina from a small Northern Texas town emailed me to thank me for this one. It must be good.
- Answer Keys - These are for all the unlocked materials above.
When writing and solving these problems I had to draw pictures as prompts. It might help you.
- Homework 1 - Nick goes to the mall. He purchased some clothes and toys for $140. He purchased the clothes for $60. He also bought 2 toy planes. Both planes cost the same amount. Write an equation to help you determine the price of one plane.
- Homework 2 - Anthony had $25 dollars to spend on chocolate covered strawberries. After buying 10 strawberries, he had $2.50 left. How much did each strawberry cost?
- Homework 3 - Lisa wants to purchase a handbag and sunglasses. She has $750. She buys one handbag for $450 and 2 pairs of sunglasses. Each pair of sunglasses costs the same price. Determine the price of one pair of sunglasses.
Standard algebra, a fractional algebra problem, and two word problems.
- Practice 1 - Christina goes shopping on Saturday. She has $150. After buying 5 hair clips, she only had $40 left. How much did each hair clip cost?
- Practice 2 - Chris goes to the cafe. He has $50. After he ordered 2 Megacappuccino, he had $6 left. How much did each Mega-cappuccino cost?
- Practice 3 - Katie goes shopping with her friend. She has $75. After buying 2 tees, she had $10 left. How much did each tee cost?
Math Skill Quizzes
The word problems can be a bit overwhelming for some students. Help them break it down.
- Quiz 1 - Ana purchased some jewelry for $160. She purchased a broach for $90. She also bought 5 pairs of earrings. The earrings were all the same price. Write an equation to help you determine the price of 1 pair of earrings.
- Quiz 2 - Daniel had $190 dollars to spend on jackets. After buying 2 jackets, he had $20 left. How much did each jacket cost?
- Quiz 3 - Nelson goes to the mobile phone shop. He purchased a phone and an SD card for $1,000. He purchased the phone for $850. He also bought 3 SD cards. Each SD card costs the same amount. Write an equation to help you determine the price of 1 SD card.
How to Write Word Problems as Equations
Most of the time when a student hears 'word problems,' there is an immediate panic observed. Take it from me, they are not as bad as you think. You will often come across story-based problems that are not simple and straight forward. They will require you to write an expression to model and eventually solve them. There are a few rules, and a system, if followed correctly, can make you make this much easier for you. Here are a few steps that you need to follow:
1. Read the problem properly, completely, and multiple times. Sometimes, a problem involves multiple variables, and the data is not easier to comprehend in just a single read. Therefore, it is recommended you give word problems multiple reads.
2. Assign variables to each unknown quantity mentioned. Assigning variable each unknown quantity can help put things into the right perspective.
3. Write down what each variable represents.
4. Re-read the problem and try to form a logical equation based on the provided data.
5. Solve the equation for the unknown variable.
6. Once the unknown variable has been identified try putting it back into the equation and see if it justifies the logic of the equation.
We will work through all the steps to solve an example problem:
Example Word Problem
Elroy has 5 boxes that he needed to ship to his brother in Nevada. The total cost for shipping all the boxes was $90. The largest box cost $30 to ship. All the remaining boxes were the same size and cost the same amount to ship. Write an equation to represent the cost of shipping all the boxes to Elroy’s brother and determine the price to ship one of the other boxes.
We start out by defining all that we are given in the problem:
$90 is the total cost. So, this would be by itself on the other side of the equals sign.
$30 was the cost of the large box. This is a constant.
All 4 other boxes cost the same amount to ship. We can state that as 4x, with x representing the cost to ship one of the smaller boxes.
The equation would therefore be: 90 = 4x + 30
If we solve for x, we can determine the cost of one box. Here are the steps to determining that value:
90 = 4x + 30 (subtract -30 from both sides)
60 = 4x (divide both sides by 4)
15 = x
This means that each of the small boxes were $15 to ship each.