Free Simple Equations Subjective Test 01 Practice Test - 7th grade

Question 1

Write the equation $p + 4 = 15$ in statement form. [1 MARK]

SOLUTION

Solution :
The sum of numbers $p$ and $4$ is $15$ .

Question 2

One-fourth of a number is 3 more than 7. Find the number. [2 MARKS]

SOLUTION

Solution : Framing of equation: 1 Mark
Solution: 1 Mark

Let us take the unknown number to be $y$ .
One-fourth of $y$ is $\frac{y}{4}$ .
This number $\frac{y}{4}$ is more than 7 by 3.
Hence we get the equation for $y$ as $\frac{y}{4} - 7 = 3$
$\Rightarrow \frac{y}{4} - 7 = 3$
$\frac{y}{4} = 3 + 7 = 10$
$∴ y = 40$

Question 3

What is the difference between an equation and an expression? [2 MARK]

SOLUTION

Solution :
Definition of Each: 1 Mark

A combination of variables and constants connected by the arithmetic operators such as addition(+), subtraction(-), multiplication(x) and division(÷) is called an expression.
e.g. $(3 x - 7)$ is an expression.

An equation is a mathematical statement wherein two expressions are set equal to each other.
e.g. $(3 x - 7) = 65$ is an equation.
$(3 x - 7) = 6 y + 8$ is an equation.

Question 4

(a) If 5z + 27 = 3z + 33, find the value of z. [2 MARKS]
(b) If 7x + 14 = 34 - 3x, find the value of x.

SOLUTION

Solution :
Each part: 1 Mark

(a) $5 z + 27 = 3 z + 33$

$\Rightarrow 5 z - 3 z = 33 - 27$

$\Rightarrow 2 z = 6$

$\Rightarrow z = 3$

$∴ z = 3.$

(b) $7 x + 14 = 34 - 3 x$

$\Rightarrow 7 x + 14 = 34 - 3 x$

$\Rightarrow 7 x + 3 x = 34 - 14$

$\Rightarrow 10 x = 20$

$∴ x = \frac{20}{10} = 2$

Question 5

(a) Find x for the following equation: 4x + 10 = 20

(b) Write an equation for the following case:
Irfan says that he has 7 marbles more than five times the marbles Parmeet has. Irfan has 37 marbles. (Take 'm' to be the number of Parmeet’s marbles.) [2 MARKS]

SOLUTION

Solution :
Solution: 1 Mark each

(a) $4 x + 10 = 20$

Dividing all the terms by 2, we get

$2 x + 5 = 10$

$\Rightarrow 2 x = 5$

$\Rightarrow x = \frac{5}{2}$

$\Rightarrow x = 2.5$

(b) Let the number of marbles Parmeet has = $m$

No. of marble Irfan has in terms of $m$ = $5 m + 7$

Given that Irfan has 37 marbles, the equation so formed will be

$\Rightarrow 5 m + 7 = 37$

Question 6

Write the equations for the following relations and find the unknown values: [3 MARKS]

a) One-third of a number plus 5 is 8.

b) A number is multiplied by 4 and the product is added to 8 to get double the original number.

c) The difference between three times $x$ and 11 is 31.

SOLUTION

Solution :
Each part: 1 Mark

The equations are as follows:

a) Let the number be $x$
$\frac{x}{3} + 5 = 8$ .
$\frac{x}{3} = 8 - 5$ .
$\frac{x}{3} = 3$ .
$x = 9$ .

b) Let the number be $x$
$(4 \times x) + 8 = 2 \times x$ .
   $4 x + 8 = 2 x$ .
   $4 x - 2 x = - 8$ .
   $2 x = - 8$ .
   $x = - 4$

c) $(3 \times x) - 11 = 31$ .
$3 x - 11 = 31$ .
$3 x = 31 + 11$ .
$3 x = 42$ .
$x = 14$ .

Question 7

(a) What is the value of x in the figure given below if it is known that perimeter of the triangle is 86?

(b) Frame an equation for the following case and find the value of the unknown:
In an isosceles triangle, the vertex angle is twice of either base angles. (Let the base angle be b in degrees. Remember that the sum of angles of a triangle is 180 degrees). [3 MARKS]

SOLUTION

Solution :
(a) 1 Mark
(b) Framing the equation: 1 Mark
Solution: 1 Mark

(a) Since it is a triangle, the perimeter of a triangle is equal to the sum of all the sides of the triangle.

So, $x + (x + 3) + 41 = 86$

$\Rightarrow 2 x + 44 = 86$

$\Rightarrow 2 x = 42$

$\Rightarrow x = 21$ .

(b) Let the base angle be $b^{\circ}$
Let the vertex angle be $a^{\circ}$
In an isosceles triangle base angles are equal.
$∴ a^{\circ} + b^{\circ} + b^{\circ} = 180^{\circ}$

$2 b^{\circ} + b^{\circ} + b^{\circ} = 180^{\circ} \Rightarrow$ Given that vertex angle is twice the base angle.

$∴ 4 b^{\circ} = 180^{\circ}$

$b^{\circ} = (\frac{180}{4})^{\circ}$

$b^{\circ} = 45^{\circ}$

Question 8

Arjun has thrice as much money as Prateek, and Shubhendu has half as much as Arjun and Prateek put together. If Arjun has 120 rupees, then how much money do Prateek and Shubhendu have? [3 MARKS]

SOLUTION

Solution :
Framing the equation: 1 Mark
Steps: 1 Mark
Result: 1 Mark

Let Prateek have x rupees.

Then, Arjun will have = 3 times Prateek = 3x

Shubhendu has half as much as Prateek and Arjun put together

Or, Shubhendu has $\frac{x + 3 x}{2} = 2 x$

According to the question,

$3 x = 120$

Or, $x = 40$

Arjun has 120 rupees, Prateek has 40 rupees and Shubhendu has 80 rupees.

Question 9

Check whether the following are satisfying the condition of a simple equation? [3 MARKS]

a) $6 x + \frac{4 x}{3} + 4$

b) $2 t + 34 = 42$

c) $2 x^{2} + 4 x + 2 = 0$

SOLUTION

Solution :
1 Mark each

a) No; It is an expression not equation because it does not have "=” sign in it.

b) Yes; It is an equation because "=” sign is present in it.

c) No; In a simple equation, the highest degree of the polynomial is one whereas here the highest power is 2.

Question 10

In a triangle ABC, angle A is half of B and angle C is thrice of A. Find the value of angle A, B and C? [4 MARKS]

SOLUTION

Solution :
Concept: 1 Mark
Framing of the equation: 1 Mark
Steps: 1 Mark
Result: 1 Mark

Let the value of angle B be $y^{\circ}$

Then, value of angle $A = \frac{y^{\circ}}{2}$

And, value of angle $C = \frac{3 y^{\circ}}{2}$

We know that sum of all angles in a triangle is $180^{\circ}$ .

$\Rightarrow y^{\circ} + \frac{y^{\circ}}{2} + \frac{3 y^{\circ}}{2} = 180^{\circ}$

$\Rightarrow 3 y^{\circ} = 180^{\circ}$

$\Rightarrow y^{\circ} = 60^{\circ} =$ Value of angle B

So, Value of angle $A = \frac{y^{\circ}}{2} = 30^{\circ}$

Value of angle $C = \frac{3 y^{\circ}}{2} = 90^{\circ}$ .

Question 11

63 cookies are distributed among four children Ram, Arjun, John, and Imran in such a way that Arjun gets twice the number of cookies than Ram. John gets half of the sum of cookies that Arjun and Ram got. Imran gets half of the number of cookies that John got. Find the number of cookies that each one received. [4 MARKS]

SOLUTION

Solution :
Framing the equation: 1 Mark
Steps: 2 Marks
Result: 1 Mark

Let the no. of cookies with Ram be y.

According to question, no. of cookies Arjun has = 2 times Ram = $2 y$

No. of cookies John has = Half of sum of Ram and Arjun. = $\frac{y + 2 y}{2}$

And, the number of cookies Imran has $= \frac{J o h n}{2}$

Since, total number of cookies = 63

$y + 2 y + (\frac{y + 2 y}{2}) + (\frac{(\frac{y + 2 y}{2})}{2}) = 63$

$\Rightarrow 3 y + \frac{3 y}{2} + \frac{3 y}{4} = 63$

$\Rightarrow \frac{12 y + 6 y + 3 y}{4} = 63$

$\Rightarrow 21 y = 63 \times 4$

$\Rightarrow y = 12$

So, No. of cookies Ram got $y = 12$

No. of cookies Arjun got $2 y = 24$

No. of cookies John got $\frac{y + 2 y}{2} = 18$

No. of cookies Imran got = 9

Question 12

A carton has twenty chocolates worth rupees 100. It has Cadbury shots worth rupees 3 each and 5-star worth rupees 11 each. How many 5 star chocolates are there in the carton? [4 MARKS]

SOLUTION

Solution :
Framing the equation: 1 Mark
Steps: 2 Marks
Result: 1 Mark

Let the no. Of Cadbury shots $= y$

Then no. of 5-star chocolates $= 20 - y$

As given in the question, Cadbury shots worth rupees 3 and 5-star worth rupees 11.

Total cost of Cadbury shots is
$= N o . o f s h o t s \times c o s t o f e a c h = 3 \times y = 3 y$

Total cost of 5 star is
$= N o . o f 5 s t a r \times c o s t o f e a c h = (20 - y) \times 11 = 220 - 11 y$

Total worth of chocolates in carton $= 100$

$\Rightarrow 3 y + 220 - 11 y = 100$

$\Rightarrow 220 - 100 = 11 y - 3 y$

$\Rightarrow 120 = 8 y$

$\Rightarrow y = 15$

There are 15 Cadbury shots and 5 5-star.

Question 13

Which of the following is a linear (or simple) equation in one variable? Give reasons. [4 MARKS]

(i) $x^{2} = 5$

(ii) $x + y = 4$

(iii) $x + 6 = 9$

(iv) $x^{2} + y^{2} = 9$

SOLUTION

Solution : 1 Mark each

(i) $x^{2} = 5$ is not a linear equation since the highest exponent of the variable is 2.

(ii) $x + y = 4$ has two variables in it. So, it is not a linear equation.

(iii) $x + 6 = 9$ is a linear equation in one variable.

(iv) $x^{2} + y^{2} = 9$ has two variables in it, and the highest exponent is 2. So, it is not a linear equation.

Question 14

What is the value of the unknown in the following equations? [4 MARKS]

(i) $2 x + 4 = 10$

(ii) $11 x - 7 = 5 (x + 7)$

(iii) $7 m + \frac{19}{2} = 13$

(iv) $2 y + \frac{5}{2} = \frac{37}{2}$

SOLUTION

Solution : Each part: 1 Mark each

(i) $2 x + 4 = 10$

$\Rightarrow 2 x = 10 - 4$

$\Rightarrow 2 x = 6$

$\Rightarrow x = \frac{6}{2} = 3$

(ii) $11 x - 7 = 5 (x + 7)$

$\Rightarrow 11 x - 7 = 5 x + 35$

$\Rightarrow 11 x - 5 x = 35 + 7$

$\Rightarrow 6 x = 42$

$\Rightarrow x = \frac{42}{6} = 7$

(iii) $7 m + \frac{19}{2} = 13$

$7 m = 13 - \frac{19}{2}$

$7 m = \frac{26 - 19}{2}$

$7 m = \frac{7}{2}$

$m = \frac{7}{2 \times 7}$

$m = \frac{1}{2}$

(iv) $2 y + \frac{5}{2} = \frac{37}{2}$

$2 y = \frac{37}{2} - \frac{5}{2}$

$2 y = \frac{37 - 5}{2}$

$2 y = \frac{32}{2}$

$y = \frac{32}{4}$

$y = 8$

Question 15

Complete the last column of the table: [4 MARKS]
$\begin{matrix} S . N O & E q u a t i o n & V a l u e & S a y, w h e t h e r t h e e q u a t i o n i s s a t i s f i e d . (y e s / N o) (i) & x + 3 = 0 & x = 3 (i i) & x + 3 = 0 & x = 0 (i i i) & x + 3 = 0 & x = - 3 (i v) & x - 7 = 1 & x = 7 (v) & x - 7 = 1 & x = 8 (v i) & 5 x = 25 & x = 0 (v i i) & 5 x = 25 & x = 5 (v i i i) & 5 x = 25 & x = - 5 \end{matrix}$

SOLUTION

Solution : Correct Answer = 0.5 Mark each

$\begin{matrix} S . N O & E q u a t i o n & V a l u e & S a y, w h e t h e r t h e e q u a t i o n i s s a t i s f i e d . (y e s / N o) (i) & x + 3 = 0 & x = 3 & N o (i i) & x + 3 = 0 & x = 0 & N o (i i i) & x + 3 = 0 & x = - 3 & Y e s (i v) & x - 7 = 1 & x = 7 & N o (v) & x - 7 = 1 & x = 8 & Y e s (v i) & 5 x = 25 & x = 0 & N o (v i i) & 5 x = 25 & x = 5 & Y e s (v i i i) & 5 x = 25 & x = - 5 & N o \end{matrix}$

Free Simple Equations Subjective Test 01 Practice Test - 7th grade

Question 1

SOLUTION

Question 2

SOLUTION

Question 3

SOLUTION

Question 4

SOLUTION

Question 5

SOLUTION

Question 6

SOLUTION

Question 7

SOLUTION

Question 8

SOLUTION

Question 9

SOLUTION

Question 10

SOLUTION

Question 11

SOLUTION

Question 12

SOLUTION

Question 13

SOLUTION

Question 14

SOLUTION

Question 15

SOLUTION

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