Word Problems leading to Algebraic Expression

Algebraic Expression from Word Problems 

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In mathematics, word problems leading to algebraic expressions simply involves translating written sentences and numerical relationships into mathematical symbols such as addition, subtraction, multiplication, division and so on.

Using the variable x, Below are some word expression phrase and their algebraic expressions:

• Six times a number: This means: 6 × x = 6x.

• Six is added to a number: This means: x + 6.

• Six less than a number: This means: x - 6.

• One fifth of a number = 1x/5 or x/5.

• Six more than double a number: This means: 2x + 6.

• The sum of six consecutive numbers: x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5).

• Three times a number subtracted from six: This means: 6 - 3x.

• More than, sum, altogether, or increased by means addition.

• Difference, less than, decreased by, or reduced by means subtraction.

• Times, product of, doubled, twice, or 'of' means multiplication.

• Divided by, ratio, per, or quotient means division.

Please read on the use of BODMAS in mathematics here.

Please read on word problems in fractions here.

 

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Steps in Solving Algebraic Problems 

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Below are steps in solving word algebraic problems:

1. Read the word problem carefully and understand it.

2. Identify the unknown value by making it a variable. This variable can be x, y, z or any alphabet.

3. Determining the operational phrase in the word problem. For instance, six times a number implies 6 × x = 6x.

4. Carefully translate the keywords in the word problem into an algebraic or mathematical expression.

Please read on multiplication and division in algebra here.

 

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Worked Examples on Word Problems leading to algebraic expressions

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Example 1

• 180 people attended a meeting. There are n men and n women, and the rest are children. How many children attended the meeting?

Solution

Let the number of children who attended the meeting be x.

The number of men = n

The number of women = n

Total umber of people who attended the meeting = 180

Therefore, x + n + n = 180

Add like terms

x + 2n = 180

• Answer: x = 180 - 2n

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Example 2

• The table below shows the number of goals for' and against a team during four weeks of a month.

Weeks	Goals For	Goals Against
1	x	2y
2	2x	y
3	3x	y
4	y	x

 

Calculate:

• The 'goals for' in a month.

• The 'goal against' in a month

Solution

'Goals For' in a month = Addition of all the goals for in the above table:

x + 2x + 3x + y

Add like terms

• Answer = 6x + y

 

'Goals Against' in a month = Addition of all the goals against in the above table:

2y + y + y + x

Add like terms

• Answer = 4y + x

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Example 3

• A pen cost h naira and a pencil cost 9 naira less than a pen. Find the cost of a pen and a pencil.

Solution

Cost of pen = h Naira

Cost of the pencil = (h - 9) Naira

Cost of a pen and a penal = h + (h - 9) Naira

Open the bracket by multiplying its content with the plus sign

h + h - 9

Addid like terms

• Answer: 2h - 9 Naira

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Example 4

• A pen cost h naira and a pencil cost 9 naira more than a pen. Find the cost of a pen and a pencil.

Solution

Cost of pen = h Naira

Cost of the pencil = (h + 9) Naira

Cost of a pen and a penal = h + (h + 9) Naira

Open the bracket by multiplying its content with the plus sign

h + h + 9

Add like terms

• Answer: 2h + 9 Naira

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Example 5

• The greater of two consecutive numbers is x.

Find the sum of the two numbers

Subtract the sum of the two numbers from 5x.

Solution

Let the first consecutive number be y

The greater consecutive number (second number) from the question is x

Sum of the consecutive numbers

• Answer = y + x

Subtract the sum of the two numbers from 5x.

5x - (y + x)

Open the bracket by multiplying its content with the minus sign

5x - y - x

Rearrange by collecting like terms

5x - x - y

• Answer = 4x - y

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Example 6

• The middle of three consecutive numbers is b. Find:

The other two numbers.

The sum of the three numbers.

Solution 

Middle number = b

First number = b - 1

Third number = b + 1

Sum of the three numbers = (b - 1) + b + (b + 1)

Open the brackets by multiplying its content with the sign in front of it

b - 1+ b + b + 1

Rearrange by collecting like terms

b + b + b - 1 + 1

• Answer = 3b

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Example 7

• A girl has x Naira and her friend 300 Naira more than her.

How much money do they have altogether?

How much more money do they need so that they have 1000 Naira between them?

Solution 

The girl's money = x Naira

Her friend's money = (x + 300) Naira

Altogether, they have: x + (x + 300) Naira

Open the bracket by multiplying its content with the plus sign

x + x + 300

Add like terms

• Altogether, they have: (2x + 300) Naira

 

To find out how much more money they need to have 1000 Naira between them, subtract their current total amount from 1000 Naira

1000 - (2x + 300)

Open the bracket by multiplying its content with the minus sign

1000 -2x - 300

Rearrange and collect like terms

1000 - 300 - 2x

• Answer = 700 - 2x

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Example 8

• A father is 42 years old and his son is y years old. If the difference of their ages is 28 years, what is the value of y.

Solution 

Father's age = 42

Son's age = y

Difference between their ages = 42 - y

42 - y = 28

Rearrange and collect like terms 

42 - 28 = y

Answer: 14 = y or y = 14

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Example 9

• I added 18 to 3 times a number. The result is equal to 5 times the number. What is the number?

Solution 

Let the number be x

I added 18 to 3 times the number = 3x + 18

The result is equal to 5 times the number

3x + 18 = 5x

Rearrange and collect like terms 

18 = 5x - 3x

18 = 2x

Divide both sides by 2

18/2 = 2x/2

• Answer: 9 = x or x = 9.

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Example 10

• Moses' age is two-thirds of Ada's age. If the sum of the ages is 30 years, how old is Ada?

Solution 

Let Ada's age be x

Moses' age = 2/3 of Ada's age

2/3 × x = 2/3 x

Sum of their ages = 30

x + 2/3 x = 30

Solve the like terms using LCM

5x/3 = 30

Cross Multiply

5x = 3 × 30

5x = 90

Divide both sides by 5

5x/5 = 90/5

• Answer: x = 18

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Example 11

• The sum of the ages of three students is 60 years. The age of the first student is (x + 10) years; the second student is (x + 5) years while the third student is x years old. Find the age of the oldest?

Solution 

Age of first student = (x + 10)

Age of second student = (x + 5)

Age of third student = x

Sum of all their age = 60

(x + 10) + (x + 5) + x = 60

Open the brackets by multiplying its content with the sign before them

x + 10 + x + 5 + x = 60

Rearrange and collect like terms

x + x + x = 60 - 10 - 5

3x = 45

Divide both sides by 3

3x/3 = 45/3

x = 15

Age of the first student = (x + 10)

15 + 10 = 25

Age of the second student= (x + 5)

15 + 5 = 20

Age of the third student = x = 15

• Therefore, age of the oldest student is 25

Please read on addition and subtraction in algebra here.

You can read on the conversion of fractions to percentages here.

You can read on the types of line in mathematics here.

 

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Assignment on Word Problems Leading to Algebraic Expression 

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1. A carpenter has two planks of wood. One plank is xcm long. and the other plank is 3xcm long. What is the total length of the two planks?

2. A shop sells x books at 500 Naira each; y books at 600 Naira each, and z books at 900 Naira each. How many books are sold attogether?

3. A saleswoman earns 19000 Naira per month. Each month, she spends 3x Naira on feed and 2x Naira on rent. How much money does she have left each month?

4. A man weighs k kilogram. He goes on a diet and loses one tenth or his weight. What is his weight after going on the diet?

5. A villager has 6 sheep and  5 goats. She sells 3x sheep and 2y goats. How many animals does she have left?

6. A man has x matches in a matchbox. On Monday, he uses one-quarter of the matches. On Tuesday he uses five more. How many matches has he used? How many has he left

7. A girl gets n Naira pocket money each week. She saves her money for five weeks and buys a present for her mother that costs 1,200 Naira. How much money does she have left?

8. A number is multiplied by 4 and then 17 is added. The result is 41. Find the number

9. Two consecutive numbers are such that twice the smaller added to the greater make a total of 52. Find the numbers.

10. A packet of candle and a box of matches cost 420 Naira. The candle cost 20 times as much as the matches. Find the cost of the matches?

11. A mand was 24 years old when his son was born. Now, he is three times as old as his son. Find the age of his son.

12. A number x multiplied by 3 and 5 is subtracted from the result. The final answer is 16. Make an equation of x and find the value of x.

13. A number is tripped and 17 is subtracted. If the result is 40, find the number?

14. A boy is older than his sister by three years. Five years ago, the ratio of their ages is 4:3. Find their present ages.

You can read on trigonometry (sine, cosine and tangent) here.

Please read on mathematics week 11 topic for jss1 first term here.

Please read on mathematics scheme of work for jss1 first term here.