Math Lesson 9.2.6 - Creating Word Problems from Equations

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Welcome to our Math lesson on Creating Word Problems from Equations, this is the sixth lesson of our suite of math lessons covering the topic of Word Problems Involving Equations, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

How to Create Word Problems from Equations?

Now, let's discuss about the inverse of what we explained earlier in this tutorial, i.e. learning how to "translate" equations into wordy problems. This is helpful, as you learn how to connect math and real - life situations.

For example, if we have the first - order equation with one variable

2x - 15 = 7

it is possible to create many wordy problems using its components. Here we present a few of them.

Two friends have an equal amount of money shared between them. If they spend $15 to buy a book, they have $7 more left. What was the original amount of money each friend had?
Two school buses were transporting students. If 15 students drop off at the first bus station and after this, only 7 students are still left in the buses, how many students did each school bus initially have?
A soccer team scored the same amount of goals in the first two rounds of the league and conceded 15 goals in total. If the goal difference at the end of the two rounds is + 7, calculate the number of goals scored by this team in each round.

In this way, we can create as many such problems as we want using the clues given in the equation.

Example 8

Which of the following scenarios is/are suitable for the equation

25 - 8x = 1

25 cakes are divided equally among 8 children in a kindergarten. If at the end only 1 chocolate is left, how many chocolates did each child receive?
25 tailors can sew 8 t - shirts each in a day. If there is 1 t - shirt left to sew, how many days did this process take to the tailors?
If 25 days ago I had eight 8 cakes in my refrigerator and yesterday (1 day ago) there were no more cakes left, how many cakes did I eat in a day?
If 8 days ago I had 25 cakes in my refrigerator and now there is only one cake left, how many cakes did I eat in a day?

Solution 8

The first thing to do with these word problems is to identify the variable. In the first example, the variable is the number of chocolates each child receives. We express this variable as x. Since there are 8 children in the kindergarten, they receive in total 8x chocolates. Thus, since initially there were 25 chocolates, and the number of chocolates left is 1, we can write the corresponding equation as 25 - 8x = 1, because the initial number of chocolates - total number of chocolates distributed among children = number of chocolates left. Therefore, the first scenario fits the given equation.

We have missing information in this scenario, as we don't know what the initial plan was. We only know that 25 tailors can sew 8 t - shirts per person in a day, so we can write 25 · 8 = 200 for the total number of t - shirts sewed in one day. In addition, we know that there is only 1 t - shirt to sew, so if the initial plan was 201 t - shirts, this takes only one day for the tailors to sew them; if the initial plan was 401 t - shirts, this takes 2 days and so on. Therefore, the equation given here is not suitable to describe this situation.

The variable here is the number of cakes eaten in a day, but our equation is not suitable to describe the third scenario. The correct equation would be 25 - (8 - 1) · x = 0, or 25 - 7x = 0.

This situation can be described by using the given equation, as the variable x is the number of cakes eaten in a day. Thus, since the number of days is 8, I ate in total 8x cakes. Initially, I had 25 cakes and now I have only 1, so the equation used here is 25 - 8x = 1, which is the same as the original.

Equations Learning Material
Tutorial ID	Math Tutorial Title	Tutorial	Video Tutorial
9.2	Word Problems Involving Equations
Lesson ID	Math Lesson Title	Lesson	Video Lesson
9.2.1	One-Step Problems Using First-Order Equations
9.2.2	Two-Steps Problems Using First-Order Equations
9.2.3	Solving Problems that Involve More than Two Steps
9.2.4	Solving Word Problems through Equations
9.2.5	Equations for solving Word Problems
9.2.6	Creating Word Problems from Equations

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Equations Math tutorial: Word Problems Involving Equations. Read the Word Problems Involving Equations math tutorial and build your math knowledge of Equations
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Equations Revision Notes: Word Problems Involving Equations. Print the notes so you can revise the key points covered in the math tutorial for Word Problems Involving Equations
Equations Practice Questions: Word Problems Involving Equations. Test and improve your knowledge of Word Problems Involving Equations with example questins and answers
Check your calculations for Equations questions with our excellent Equations calculators which contain full equations and calculations clearly displayed line by line. See the Equations Calculators by iCalculator™ below.
Continuing learning equations - read our next math tutorial: Identities

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