One can learn how to solve a word problem by using a linear equation in one unknown from here. Practice as many questions as possible from the Worksheet on Solving a Word Problem by using Linear Equation in One Unknown for a better understanding of the concept. Linear Equation on One Unknown Word Problems Worksheet includes step-by-step solutions for all the problems so that you will learn the concept on a deeper level. Enhance your math proficiency by answering the different models of questions framed on the topic in the worksheet.
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Solving Linear Equation in One Unknown Worksheet PDF
Example 1.
The sum of the two numbers is 80. If one exceeds the other by 20, find the numbers?
Solution:
Let the number be x
From the given data one number exceeds the other by 20 the other number is x+20
Sum of two numbers = 85
x+x+20 =80
2x+20=80
2x=80-20
x=30
The other number is x+20
=30+20
=50
Therefore, the numbers are 30 and 50.
Example 2.
The three angles in a triangle are in the ratio of 4:3:5. Find the measure of each angle?
Solution:
We know Sum of the angles in a triangle = 1800
As per the given data, we can frame the equation as 4x+3x+5x=1800
12x=1800
x=1800/12
x=150
The three angles are in the measure of 4:3:5
Thus each angle is 4x = 4*150 =600
3x=3*150=450
5x=5*150=750
Thus, the three angles in a triangle are 600, 450, 750
Example 3.
The length of a rectangular plot exceeds its breadth by 6 meters. If the perimeter of the plot is 150. Find the dimensions of the plot?
Solution:
Let the breadth of a rectangular plot be x meters
Since length exceeds its breadth by 6 meters we have l = x+6
The Perimeter of the Rectangular Plot = 150 Meters
We know the formula of the perimeter of a rectangle = 2(l+b)
Substituting the known values in the formula of the perimeter we get
150=2(x+6+x)
150=2(2x+6)
150=4x+24
150-24=4x
136=4x
x=136/4
x=34
Thus, length = x+6
=34+6
=40 meters
Therefore, the length and breadth of the rectangular plot are 40 meters and 34 meters respectively.
Example 4.
If you add 1/2 to a number and multiply the result by 1/4, you get 1/5. What is the number?
Solution:
Let the number be x
(x+1/2)1/4 = 1/5
(2x+1)/2*1/4 = 1/5
(2x+1)/8 = 1/5
(2x+1)5=8
10x+5=8
10x=8-5
10x=3
x=3/10
Therefore, the number is 3/10
Example 5.
The base of an isosceles triangle is 3/4 cm. The perimeter of the triangle is 7 1/10 cm. What is the length of either of the remaining equal sides?
Solution:
Let x be each of the lengths of the remaining two sides of the isosceles triangle.
Thus, the sides of the triangle are x, x, 3/4 cm
Given Perimeter of the Triangle = 7 1/10 cm
x+x+3/4 = 7 1/10
2x+3/4 = 71/10
2x=71/10-3/4
2x= (142-15)/20
2x=127/20
x=(127*2)/20
=254/20
=127/10
Example 6.
A number subtracted from 7 is equal to 3 times the number. Find the number?
Solution:
Let the number be x
From given data 7-x =3x
7=3x+x
7=4x
x=7/4
Therefore, the number is 7/4
Example 7.
A farmer cuts a 300-foot fence into two pieces of different sizes. The longer piece should be five times as long as the shorter piece. How long are the two pieces?
Solution:
Let the shorter piece be x
From given data Longer Piece is 5 times long as shorter piece = 5x
Given longer piece +shorter piece = 300 foot
5x+x=300
6x=300
x=300/6
=50 foot
Longer Piece = 5x
=5*50
=250 foot
Therefore longer piece and shorter piece are of 250 foot and 50-foot length.
Example 8.
The perimeter of an equilateral triangle is 45 meters. How long is each side?
Solution:
Let us assume the side of the equilateral triangle be x meters
The Perimeter of Equilateral Triangle = 3a
3a=45
a=45/3
a=15 meters
Thus, each side of the equilateral triangle is 14 meters long.
Example 9.
If 5 blocks weigh 30 ounces, how many blocks weigh 90 ounces?
Solution:
Let us denote the weight of the block be x
5x=30 Ounces
x=30/5
=6 Ounces
How many Blocks weigh 90 Ounces =?
= 90/6
=15 blocks
Therefore, 15 blocks weigh 90 ounces
Example 10.
Ina class of 44 students, the number of girls is one-third the number of boys. Find the number of boys and girls?
Solution:
Total number of students in the class = 44
Consider Number of boys = x
Number of girls = 1/3(x)
=x/3
Sum of boys and girls = 44
x+x/3 =44
4x/3 =44
4x=44*3
4x=132
x=132/4
x=33
Number of girls = x/3
=33/3
=11
Therefore, the number of boys and girls in the class is 33 and 11 respectively.