Simple Equations(7th Grade > Mathematics ) Questions and answers for exam Preparation

7th Grade > Mathematics

SIMPLE EQUATIONS MCQs

Total Questions : 118 | Page 5 of 12 pages

Question 41. 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}

Discuss Question

:
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}

Question 42. 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

Discuss Question

:
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 43. Write the equation

p + 4 = 15

in statement form. [1 MARK]

Discuss Question

:
The sum of numbers

p

and

4

15

Question 44. One-fourth of a number is 3 more than 7. Find the number. [2 MARKS]

Discuss Question

:
Framing of equation: 1 Mark
Solution: 1 Mark
Let us take the unknown number to be

y

.
One-fourth of

y

\frac{y}{4}

.
This number

\frac{y}{4}

is more than 7 by 3.
Hence we get the equation for

y

\frac{y}{4} - 7 = 3

\Rightarrow \frac{y}{4} - 7 = 3

\frac{y}{4} = 3 + 7 = 10

∴ y = 40

Question 45. 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}

Discuss Question

:
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 46. 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.

Discuss Question

:
Each part: 1Mark
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

(3 \times x) - 11 = 31

3 x - 11 = 31

3 x = 31 + 11

3 x = 42

x = 14

Question 47. Check whether the following are satisfying the condition of a simple equation? [3 MARKS]
a)

6 x + \frac{4 x}{3} + 4

2 t + 34 = 42

2 x^{2} + 4 x + 2 = 0

Discuss Question

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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 48. 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]

Discuss Question

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

Discuss Question

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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 50. (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]

Discuss Question

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Solution: 1 Mark each
(a)