## ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 9 Linear Equations and Inequalities Check Your Progress

Question 1.

Solve the following equations :

(i) 2 (x – 5) + 3 (x – 2) = 8 + 7 (x – 4)

Solution:

(i) 2 (x – 5) + 3 (x – 2) = 8 + 7 (x – 4)

Removing group symbols,

2x – 10 + 3x – 6 = 8 + 7x – 28

⇒ 5x- 16 = 7x – 20

⇒ 5x – 7x = – 20 + 16

(Transposing -16 to R.H.S and 7x to L.H.S)

⇒ -2x = -4

⇒ x = 2

Question 2.

A number exceeds its three-fifth by 22. Find the number.

Solution:

Let the number be x

Three-fifth of a number = \(\frac { 3 }{ 5 }\) x

According to statement,

Question 3.

When 9 is added to twice a number, the result is 3 more than thrice the number. Find the number.

Solution:

Let the number be x

Twice a number = 2x

Thrice a number = 3x

According to statement,

9 + 2x = 3 + 3x

⇒ 9 – 3 = 3x – 2x

⇒ 6 = x

⇒ x = 6

Question 4.

The ten’s digit of a two digit number is twice the unit’s digit. The sum of the number and its unit’s digit is 66. Find the number.

Solution:

Let the unit’s digit be x.

Ten’s digit = 2x.

The number =10 × 2x + x = 20x + x

According to statement,

10 × 2x + x + x = 66

⇒ 20x + x + x = 66

⇒ 22x = 66

⇒ x = 3

The number = 20x + x = 20 × 3 + 3 = 60 + 3 = 63

Question 5.

A student bought some pens at ₹ 8 each and some pencils at ₹ 1.50 each. If the total number of pens and pencils purchased is 16 and their total cost is ₹ 50, how many pens did he buy?

Solution:

The total number of pens and pencils purchased = 16

Let the number of pens bought = x

The number of pencils bought = 16 – x

Cost of pens bought = 8x

Cost of pencils bought = 1.50 (16 – x)

According to given condition,

8x + 1.50 (16 – x) = ₹ 50

⇒ 8x + 24 – 1.50x = 50

⇒ 6.50x = 50 – 24

⇒ x = \(\frac { 26 }{ 650 }\) × 100 = 4

No. of pens bought = 4

Question 6.

Arvind is eight years older than his sister. In three years, he will be twice as old as his sister. How old are they now?

Solution:

Let the sister’s age = x years

Arvind’s age = (x + 8) years.

In three years, sister’s age = (x + 3) years

In three years, Arvind’s age = (x + 8 + 3) years

According to statement,

x + 8 + 3 = 2(x + 3)

⇒ x + 11 = 2x + 6

⇒ x – 2x = 6 – 11

⇒ -x = -5

⇒ x = 5.

Sister’s age = 5 years

Arvind’s age = 5 + 8 = 13 years.

Question 7.

The angles of a triangle are in the ratio 1 : 2 : 3. Find their measure in degrees.

Solution:

Let the angles of a Δ are x, 2x and 3x.

We know that

Sum of ∠s of a Δ is 180°

x + 2x + 3x = 180°

⇒ 6x = 180°

⇒ x = 30°

∠s of a Δ are

1x = 1 × 30° = 30°,

2x = 2 × 30° = 60°,

and 3x = 3 × 30° = 90°

Question 8.

Solve the following inequations and represent their solution on a number line:

Solution: