Simple Linear Equations Test - 1

2(x + 1) – 5 = –x + 7

⇒ 2x + 2 – 5 = –x + 7

⇒ 2x – 3 = –x + 7

⇒ 2x + x = 7 + 3                                 [Transposing x to L.H.S. and 3 to R.H.S]

⇒ 3x = 10

Dividing both sides of the equation by 3,

X= 10/3

Thus, the value of x in the given equation is10/3.

It is given that the numbers x and y are in the ratio 4:5 and the value of y is 5p.

∴ x = 4p

It is also given that z is 5 less than x.

∴ z = x − 5 = 4p − 5

The sum of the three numbers is 60.

∴ x + y + z = 60

⇒ 4p + 5p + 4p − 5 = 60

Thus, the equation 4p + 5p + 4p − 5 = 60 correctly represents the given situation.

It is given that the cost of each pen is Rs 5.

∴ Cost of 6 pens = Rs 5 × 6 = Rs 30

Also, the cost of each notebook is Rs C.

∴ Cost of 5 notebooks = Rs C × 5 = Rs 5C

⇒ Cost of 5 notebooks and 6 pens = (5C + 30)

It is given that the cost of 5 notebooks and 6 pens is Rs 180.

∴ 30 + 5C = 180

Thus, the equation, 30 + 5C = 180, is the required equation, which represents the given situation.

Runs scored by the batsman = r

Then, twice the runs scored by the batsman = 2r

It is given that twice the runs scored by the batsman are 14 more than a century.

A century = 100

Therefore, 2r − 14 = 100

Thus, the equation which represents the given statement is 2r − 14 = 100

The present age of Rahim and Ram are in the ratio 11: 6.

Then, let the present age of Rahim and Ram be 11x and 6x respectively.

Six years ago, Rahim’s age was (11x − 6) and Ram’s age was (6x − 6).

∴ 11x − 6 = 2 (6x − 6)

⇒ 11x − 6 = 12x − 12

⇒ 12 − 6 = 12x − 11x

⇒ x = 6

∴ Ram’s present age = 6x = 6 × 6 = 36

Thus, Ram’s present age is 36 years.

Length of each side of the square = 45 cm

∴ Perimeter of the square = 4 × 45 cm = 180 cm

Length of the rectangle = x

∴ Width of the rectangle = x − 10 cm

∴Perimeter of the rectangle = 2 × (x + x − 10) cm

It is given that the perimeter of the square equals that of the rectangle.

Thus, the equation that correctly represents the given situation is

2 × (x + x − 10 cm) = 180 cm.