Linear Equations in One Variable Test - 2

Let the two consecutive even numbers be x + 2 and x + 4.

Given, the sum of two consecutive even numbers is 90.

Therefore, the required equation will be

(x + 2) + (x + 4) = 90

2x + 6 = 90

2x = 84

x = 42

Thus, the smaller number = x + 2 = 42 + 2 = 44

When we add or subtract the same number on both sides of a linear equation,

the balance of the equation remains undisturbed.

Thus, adding 5 to both sides of equation 3x = x - 1, we get

3x + 5 = x - 1 + 5

3x + 5 = x + 4

3x = x + 4 - 5

3x = x - 1

Since x = -1 is a solution of the equation 6x + 6 = 0, we have

6x + 6 = 6(-1) + 6 = -6 + 6 = 0

Let the digit at unit's place be x.

Then, digit at ten's place = 11 - x

According to given information,

10x + (11 - x) = 10(11 - x) + x - 45

10x + 11 - x = 110 - 10x + x - 45

9x + 11 = 65 - 9x

18x = 54

x = 3

Thus, the digit at the unit's place of the original number is 3.

Let the one number be x.

then, the other number = 12 - x

As per the given information, we have

3x + 5(12 - x) = 44

3x + 60 - 5x = 44

-2x + 60 = 44

-2x = 44 - 60

-2x = -16

x = 8

Hence, other number = 12 - x = 12 - 8 = 4

Thus, the two numbers are 4 and 8.

Let x be the length of a rectangle.

Perimeter of a rectangle = 2(Length + Breadth)

Therefore,

64 = 2(x + 15)

64 = 2x + 30

2x = 34

x = 17

Thus, the length of a rectangle is 17 cm.

Amit's present age = 20 years

Leela's present age = 4 years

Let after x number of years, Amit be twice as old as Leela.

After x years, Amit's age = (20 + x) years

After x years, Leela's age = (4 + x) years

Then,

20 + x = 2(4 + x)

20 + x = 8 + 2x

20 - 8 = 2x - x

x = 12

Thus, after 12 years Amit will be twice as old as Leela.

Let Mona's present age = x years.

Then, her father's present age = 3x years

After 12 years,

Mona's age = (x + 12) years

Her father's age = (3x + 12) years

According to the given information,

3x + 12 = 2(x + 12)

3x + 12 = 2x + 24

x = 12

then, 3x = 3(12) = 36

Thus, Mona's present age is 12 years and her father's present age is 36 years.

Let the two-digit number be xy = 10x + y

From the given conditions, we have

x + y = 10        ….(1)

10y + x = 10x + y - 36

10y - y - 10x + x = -36

9y - 9x = -36

9(y - x) = -36

y - x = -4

x - y = 4          ….(2)

Adding (1) and (2), we get

2x = 14

x = 7

From (1), y = 10 - 7 = 3

Therefore, number = xy = 73

Thus, the ten's place of the original number is 7.

2x + 4 = x + 8

2x - x = 8 - 4    [By transposition]

x = 4