linear equations in one variable class 8 worksheets

Let x,x+1 ,x+2 are three consecutive integers in increasing order
Then according to question
$2(x) + 3(x+1) + 4(x+2) =56$
$2x + 3x +3 + 4x + 8 =56$
$9x + 11 =56$
$9x = 56 -11$
$9x = 45$
x=5

So,numbers are 5,6,7

Let breadth be x
Then length =2x + 2
According to Question
Perimeter =154 m
$2(L + B) = 154$
$2( 2x+2 + x)=154$
$2(3x + 2)=154$
$6x + 4 =154$
$6x= 150$
x= 25 m
So Length =52 m and breadth =25 m

Let one number be x, then other number will be x +15
According to question
Sum of numbers=95
$x + x + 15=95$
$2x+15=95$
$2x=95-15$
$2x=80$
$x=40$
So, the two numbers are 40 and 55

When the numbers are in ratio, we assume numbers as the value in ratio multiplied by variable
So, Let numbers be 4x and 3x
Now Difference of numbers =18
$4x -3x=18$
$x=18$

So,numbers are 72 and 54

Let x,x+1 ,x+2 are three consecutive integers
Now sum of these=57
$x + x + 1 + x +2=57$
$3x + 3=57$
$3x=54$
$x=18$
So, numbers are are 18,19,20

Let lenght and breadth are 11x and 4x
Perimeter of plot = 2(L+ B) = 2(11x + 4x)=30x

Now given
$100 \times 30x = 75000$
$3000x=75000$
$x= \frac {75000}{3000}$
$x=25 m$
So, lenght and breadth are $11 \times 25= 225 m$ and $4 \times 25= 100 m$

a. $x +3 =11$
b. $x- 2=15$
c. $3x -2=4$
d. 2(x+ 7) =13

Let x be the number,then

$ 8(x - \frac {5}{2}) = 3x$
$ 8x - 20 =3x$
$ 8x -3x = 20$
$5x = 20$
$x=4$

Let x be the number , then other number will be x + 12
According to question
$x+ x +12=48$
$2x + 12=48$
$x=18$
So, the numbers are 18 and 30

Let x,x+1 ,x+2 are three consecutive integers
Now sum of these=51
$x + x + 1 + x +2=51$
$3x + 3=51$
$3x=48$
$x=16$
So, numbers are are 16,17,18

Let her younger sister age is x, the Jane age is x + 6
After 10 years, Jane age will be $x+6 + 10=x+16$ and sister age will be $x +10$
Now ,
$x+16 + x +10=50$
$2x + 26=50$
$2x=24$
$x=12$

So, Jane age is 18 years and her sister age is 12 years

Let numerator be x ,then denominator is x + 8 and fraction is $\frac {x}{x+8}$
If the numerator is increased by 17, New numerator becomes $x+17$
If denominator is decreased by 1, New denominator becomes $x +8 -1 =x+7$
Now
$\frac {x + 17}{x+7} = \frac {3}{2}$
By cross multiplication
$2(x+17) = 3(x+7)$
$2x + 34 = 3x +31$
$ 3x +31=2x + 34 $
$ 3x -2x = 34 -31$
$x =3$
So fraction is $\frac {3}{11}$

Let x be the type of Prize Rs 100.
Since the total number of prize is 63, Rs 25 type will be 63 -x
Now according to Question,
The value of these total prizes = Rs 2700
$100 \times x + (63 -x) \times 25 = 2700$
$ 100x + 1575 -25 x = 2700$
$ 75x = 2700 -1575$
$75x = 1125$
$x=15$
So 15 Rs 100 type prize and 47 Rs 25 type prizes were present

Let x be the base angle
Now
$ x +x + 80 = 180$
$2x =100$
$x=50$

a. True
b. True
c. False , x=25
d. True
e. False . Correct numbers are 7x,7x+7, 7x+14

Let x be the current age
Age after 15 years =x + 15
Now
$x+ 15 = 4x$
$ 4x= x + 15$
$ 4x -x =15$
$ 3x=15$
$x=3 years$

Let the number of notes are 2x,3x and 5x
$ 100 \times 2x + 50 \times 3x + 10 \times 5x = 400000$
$200x + 150 x + 50x =400000$
$400x = 400000$
$x= 1000$
So ,Banks as 2000 100’s notes,3000 50’s notes and 5000 50’s notes

$2x+3 +5x +1 + 5x+2=30$
$12x=30-6=24$
$x=2$
So sides are 7,11,12