In linear algebra, there are many problems which are combination of known and unknown values. Linear equations in one variable is a combination of one variable and one constant(mostly). The standard form of such equation looks like ax + b = 0, where a $\neq$ 0. Linear equations helps us to solve our many real life problems as well. It is a little difficult to solve problems stated in words and such type of problems are known as word problems. In this section will learn how to convert statements into equations and solve them to get an answer.
Linear Equations in One Variable Word Problems
Below word problems based on linear equations in one variable have been prepared by subject experts based on the latest syllabus. We provided step-by-step explanation to every question which help students how to convert statements into algebraic expressions and solve them.Problem 1
: The sum of two numbers is 50. One of the numbers lesser than the other by 6. Find the numbers.
Let n be first number, then second number be n - 6.
Sum of two numbers = 50 (given)
so n + (n - 6) = 50
Simplify the above equation for n.
n + n - 6 = 50
2n - 6 = 50
2n = 50 + 6
2n = 56
n = 56/2 = 28
First number = 28
Second number = n - 6 = 28 - 6 = 22
Kevin is 7 years older than Novita. Three years later, Kevin will be twice as old as Novita. Find their present ages.Solution
: Let x be the Novita's present age
| || Novita
|Present Age || x
|| x + 7
| 3 years later|| x + 3
|| (x + 7) + 3
According to statement: Kevin's Age = 2(Novita's Age)
(x + 7) + 3 = 2(x + 3)
x + 7 + 3 = 2x + 6 (Using distributive property)
x + 10 = 2x + 6
x - 2x = 6 - 10
-x = -4
or x = 4
And, x + 7 = 4 + 7 = 11
Therefore, Present age of Novita is 4 years and present age of Kevin is 11 years.Problem 3:
The sum of two consecutive multiples of 6 is 68. What are these multiples.
Solution: Let x be the first number then second number will be x + 6
(Since we are asked to find two consecutive multiples of 6)
According to statement: x + (x + 6) = 68
x + (x + 6) = 68
2x + 6 = 68
2x = 68 - 6
2x = 62
2x/2 = 62/2
x = 31
Again, x + 6 = 31 + 6 = 37
Required numbers are 31 and 37.
Steps for Solving Linear Equations in One Variable
Steps to follow in solving a linear equation in one variable word problems:
1. Read the given problem carefully and note down given points.
2. Denote the unknown by any variable say x, y.
3. Translate the statement into mathematical expression.
4. Write a linear equation in one variable.
5. Solve for unknown variable.
6. Verify your answer.
Word Problems for Practice
Problem 1: Suresh’s age is two times his daughter's age. Three years ago, his age was 3 times his daughter's age. Find their present ages.
Problem 2: One side of a rectangular card is 10 cm less than 2 times its another side. If sum of all the sides is 22 cm. Find the dimensions.
Problem 3: A number consists of two digits whose sum is 10. The digits of the numbers are reversed if we subtract 6 from the number. Find the number.
Problem 4: The sum of four consecutive odd numbers is 72. Find the numbers.