ALGEBRA WORD PROBLEMS - NUMBER OF SOLVED EXAMPLES AND EXERCISES.

Please study
Linear Equations before Algebra Word Problems,
if you have not already done so.

There, we explained solving of the Linear Equations
in one variable with a number of solved Examples.

That knowledge is a prerequisite here.

Here we deal with the Word Problems involving
Linear Equations in one variable.

We provide Links to other Word problems.

A number of word problems are worked out.
Several word problems are given for practice
in exercise with answers.

Practice makes one perfect.
This is especially true for learning of
solving Algebra Problems (Math Problems).

So, take the exercises seriously and practice solving the problems.

Algebra Word Problems involving Linear Equations in one variable

Equations are frequently used to solve practical problems.

The steps involved in the method of solving
an algebra word problem are as follows.

Step 1 :

Read the given Algebra Word Problem carefully and
note down what is given and what is required.

Step 2 :

Select a letter say x to represent
the unknown quantity asked for.

Step 3 :

Represent the word statements of the problem
in the symbolic language step by step.

Step 4 :

Look for quantities which are equal as per
conditions given and form an equation.

Step 5 :

Solve the equation obtained in step 4.

Step 6 :

Check the result for making sure that your answer
satisfies the requirements of the problem.

Example 1 of Algebra Word Problems

One number is 3 less than two times the other.
If their sum is increased by 7, the result is 37.
Find the numbers.

solution to Example 1 of Algebra Word Problems :

Let x be the other number.
Then the first number as per data is 3 less than two times x.
That means the first number is 2x - 3.
Their sum = x + (2x -3) = 3x - 3.
By data,
Increasing their sum by 7, the result is 37.
That means (3x - 3) + 7 = 37. ⇒ 3x - 3 + 7 = 37 ⇒ 3x + 4 = 37

This is the Linear Equation formed by converting
the given word statements to the symbolic language.

Now we have to solve this equation.
⇒ 3x = 37 - 4 = 33 ⇒ x = 33⁄3 = 11.
The first number = 2x - 3 = 2(11) - 3 = 22 - 3 = 19.
The numbers are 11 and 19. Ans.

Check:
Since 19 = 2(11) - 3,
"one number is 3 less than two times the other" is satisfied. (verified)
Since 19 + 11 + 7 = 37,
"If their sum is increased by 7, the result is 37" is satisfied. (verified)

Example 2 of Algebra Word Problems

If two thirds, one half and one seventh of a number is added to itself,
the result is 37. Find the number.

solution to Example 2 of Algebra Word Problems :

Let x be the required number.
Then
two thirds of the number = 2x⁄3.
one half of the number = x⁄2.
one seventh of the number = x⁄7.
As per data, sum of these added to the number i.e. x = 37.
That means 2x⁄3 + x⁄2 + x⁄7 + x = 37.

This is the Linear Equation formed by converting
the given word statements to the symbolic language.

Now we have to solve this equation.
The L.C.M. of the denominators 3, 2, 7 is 3 x 2 x 7 = 42.
Multiplying both sides of the equation by 42, we get
42(2x⁄3) + 42(x⁄2) + 42(x⁄7) + 42x = 42 x 37.
14(2x) + 21(x) + 6(x) + 42x = 42 x 37
⇒ (28 + 21 + 6 + 42)x = 1554. ⇒ 97x = 1554
⇒ x = 1554⁄97 = 16.02
The required number = 1554⁄97 = 16.02 Ans.

Check:
two thirds of the number = (2⁄3.)(1554⁄97) = (2)(518⁄97) = 1036⁄97
one half of the number = (1⁄2.)(1554⁄97) = 777⁄97
one seventh of the number = (1⁄7)(1554⁄97) = 222⁄97
the number = 1554⁄97
Sum of all these = (1036 + 777 + 222 + 1554)⁄97 = 3589⁄97
= (37 x 97)⁄97 ( Since 37 x 97 = 3589)
= 37. Which is same as per data. (verified)

More Algebra Word Problems

The following Links take you to some
more sets of Algebra Word Problems.

Set 2 Solved Examples and Exercise

Set 3 Solved Examples and Exercise

Set 4 Solved Examples and Exercise





















The above sets are all on Word Problems
on Linear Equations in one Variable.

Below are Links on Some More Algebra Word problems.

Word Problems on Linear Equations in Two variables.

Word Problems on Quadratic Equations.

Exercise on Word Problems

Solve the following Word problems.

1. Half of a certain number added to its one third makes it 20.
   What is the number?
2. Divide 42 into two parts so that one part is twice the other part.
3. Five years ago the age of a father was twice the age of his son.
   The sum of their present ages is 70 years. Find their present ages.

For More Exercise Problems of Algebra Word Problems go to
Word Problems on Linear Equations in Two variables.

Word problems on Quadratic Equations.

Answers to Exercise on Word Problems

The Answers to the Word Problems
of the exercise given above, are given below.

1. 24
2. 14, 28
3. 45 years, 25 years