Creating word problems with variables
Construct a total of six word problems that include the following:
- Adding and subtracting with variables (two word problems)
- Multiplying and dividing with variables (two word problems)
- Combining like terms (one word problem)
- Solving equations (one word problem)
CREATING WORD PROBLEMS WITH VARIABLES 2
through the problem-solving process? You can use one of your word problems as an example to
illustrate your thoughts.
Word count: 613
Question 1: Adding and subtracting with variables
1 There are 13 apples in Tom’s store. He got seven bananas from his garden to add to the
store. He sold two more apples and six grapes to add to his collection. How many fruits does
he have in store? Equation 13x + 7y -2x +6a
2 Alfred wants to buy two pencils and four books. He has been given a present by his mother
that is made of 6 books. The book store offers a discount of 5 for all the items purchased.
How many books and pencils does he have?
Question 2: Multiplying and dividing with variables
1 Angela and Martin are friends they got (X-3) 2 products from the shop down turn. Solve the
equation to get the total products that they have together.
a) X2-9
b) X2-6x+9
c) X2 +9
CREATING WORD PROBLEMS WITH VARIABLES 3
2 Mary and Sherry are coin collectors. Sherry has seven times as many coins as Mary. If
Sherry has 63 coins, how many coins does Sherry have?
Question 3: Combining two like terms
A child and adult are ailing from the same disease. The doctor wants to provide the sick
patients with a vial that contains 2 g of the suitable medicine in two dosages. The adult
requires 60mg more of the medicine when compared to the child. Explain how to administer
the medicine to each of the patients.
Question 4: Solving equations
Milk is being drained out of the cooling tank through 2 pipes with the same width positioned
at different sides at the rate of 330L per minute. The pipe on the right does drain 50 liters per
minute more than the other pipe located on the left side of the tank. Calculate the liters that
each of the two pipes on the cooling tank drain
The purpose of word problems in variability is to enable the students to relate the
lessons to their experiences. This does make it easy for them to apply the concepts.
Therefore, when creating word problems, the first aspect is to use simple language that will
help the students to understand the questions. Secondly, the use of figures in the question
where necessary to help the students summarize the problem with ease. Thirdly, the teacher
needs to mix the word problems where they combine short and long word problems. This
enables the students to find the operations that they are to use to get answers. Lastly, the
incorporation of the concept of the question (Silver, 2013).
CREATING WORD PROBLEMS WITH VARIABLES 4
In solving variables, the first step deals with reading the entire problem as one and
identifying what the question does need. The second step deals with picking terms, numbers,
and words. The third step deals with the use of letters to represent the unknown values. The
fourth step deals with breaking down the question into portions to make it easier to solve. The
sixth step deals with creating a suitable relationship to use to solve the variables. The last step
deals with going through the solution to make sure that the answer makes logical sense
(Silver, 2013). The example that will be used to illustrate the concept is question 4’s solution
done below:
Solution
Let x be the rate of the pipe draining at a slower rate
Let (x+50) be the rate of the faster pipe
Combine the two and equate them to the total L/min drained from the cooling tank
X +( X +50) = 330
Therefore:
2x + 50 =330
2x= 330-50 =2x =280
X= 140
The slower drainage pipe is 140 while the rate of the faster pipe is (x+50) where x is 140
which brings the value to 190
CREATING WORD PROBLEMS WITH VARIABLES 5
Reference
Silver, E. A. (Ed.). (2013). Teaching and learning mathematical problem solving: Multiple
research perspectives. Routledge.
