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

7th Grade > Mathematics

SIMPLE EQUATIONS MCQs

Total Questions : 118 | Page 3 of 12 pages

Question 21. What is the solution of the equation

4 x + 25 = 7 x + 10

? [2 MARKS]

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:
Steps: 1 Mark
Result: 1 Mark

4 x + 25 = 7 x + 10

Now, subtracting 10 on both sides, we get

4 x + 25 - 10 = 7 x + 10 - 10

4 x + 15 = 7 x

Now, subtracting

4 x

on both sides, we get

4 x - 4 x + 15 = 7 x - 4 x

15 = 3 x

Dividing both sides by 3, we get:

\frac{15}{3} = \frac{3 x}{3}

x = 5

Question 22. If

\frac{2 x + 1}{3 x - 2} = \frac{9}{10}

, then the value of 'x' is: [2 MARKS]

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:
Steps: 1 Mark
Result: 1 Mark

\frac{2 x + 1}{3 x - 2} = \frac{9}{10}

\Rightarrow 10 (2 x + 1) = 9 (3 x - 2)

\Rightarrow 20 x + 10 = 27 x - 18

\Rightarrow 10 + 18 = 27 x - 20 x

\Rightarrow 28 = 7 x

\Rightarrow 7 x = 28

\Rightarrow x = \frac{28}{7} = 4

The value of 'x' is 4.

Question 23. Find the number in the following cases: [4 MARKS]
a) When a number is multiplied by 6 and 4 is added to the product, it becomes 54.
b) Adding 6 to 4 times a number gives 88.

Discuss Question

:
Each part: 2 Marks
a) Let the number be

y

According to question,

(y \times 6) + 4 = 54

\Rightarrow 6 y = 54 - 4

\Rightarrow 6 y = 50

\Rightarrow y = \frac{50}{6}

b) Let the number is

y

;
According to question,

6 + 4 \times y = 88

\Rightarrow 6 + 4 y = 88

\Rightarrow 4 y = 88 - 6

\Rightarrow 4 y = 82

\Rightarrow y = \frac{82}{4}

Question 24. (a) Write the statement of the following equations. [4 MARKS]
i)

7 x + 4 = 46

ii)

\frac{5 x + 4}{6} = 13

(b) Raju’s father’s age is 5 years more than three times Raju’s age. Find Raju’s age, if his father is 44 years old.

Discuss Question

:
(a) Correct statement of equation: 1 Markeach
(b) Framing of equation: 1 Mark
Solution: 1 Mark
(a) i) When a number is multiplied with 7 and 4 is added to their product, we get 46 as the final result.
ii) When a number is multiplied with 5,4 is added to their product and their final sum isdivided by 6, the result which we get is 13.
(b) Let Raju's age be x.
Raju's father's age =

3 x + 5 = 44

\Rightarrow 3 x + 5 = 44

\Rightarrow 3 x = 44 - 5 = 39

\Rightarrow x = \frac{39}{3}

\Rightarrow x = 13 y e a r s

Raju's age is 13 years.

Question 25. Sum of two numbers is 38 and their difference is 16. Find the numbers? [3 MARKS]

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:
Framing of the equation: 1 Mark
Steps: 1 Mark
Answer: 1 Mark
Let the number be

^{'} x^{'}

.
Then, the other number is

(38 - x)

The difference between the numbers is 16.

\Rightarrow (38 - x) - x = 16

\Rightarrow 38 - 2 x = 16

\Rightarrow 38 - 16 = 2 x

\Rightarrow 2 x = 22

\Rightarrow x = 11

Other number

= 38 - x = 38 - 11 = 27

Question 26. Ethan is given the responsibility of buying a week's supply of food and medication for the dogs and cats at a local shelter. The food and medication for each dog cost twice as much as the supplies for a cat. He needs to feed 164 cats and 24 dogs. His budget is Rs. 4240. How much can Ethan spend on each dog for food and medication? [4 MARKS]

Discuss Question

:
Framing the equation 2 Marks
Steps: 1 Mark
Result: 1 Mark
Let the expenditure on a cat be

y

The expenditure on a dog

= 2 y

.
Total expenditure on cats

= 164 \times y = 164 y

Total expenditure of dogs

= 24 \times 2 y = 48 y

According to question:

164 y + 24 \times 2 y = 4240

\Rightarrow 164 y + 48 y = 4240

\Rightarrow 212 y = 4240

\Rightarrow y = \frac{4240}{212} = 20

Hence, expenditure of a dog

= 2 y = 40

So, for 24 dogs the total expenditure is

= 24 \times 40 = R s .960

Question 27. A fraction is given in which numerator is less than denominator by three. If we add number seven in the numerator and subtract one from the denominator,

\frac{3}{2}

is the new fraction which we get. Find the original fraction? [4 MARKS]

Discuss Question

:
Framing the equation: 1 Mark
Steps: 2 Marks
Result: 1 Mark
Let the numerator of a rational number

= x

Then the denominator of a rational number

= x + 3

When numerator is increased by 7, then new numerator

= x + 7

When denominator is decreased by 1, then new denominator

= x + 3 - 1

The new number formed

= \frac{3}{2}

According to the question,

\frac{x + 7}{x + 3 - 1} = \frac{3}{2}

\Rightarrow \frac{x + 7}{x + 2} = \frac{3}{2}

\Rightarrow 2 (x + 7) = 3 (x + 2)

\Rightarrow 2 x + 14 = 3 x + 6

\Rightarrow 3 x - 2 x = 14 - 6

\Rightarrow x = 8

Numerator = 8, then denominator = 8+3 = 11
Original fraction

= \frac{8}{11}

Question 28. The sum of four consecutive multiples of 9 is 378. Find these multiples? [3 MARKS]

Discuss Question

:
Framing the equation: 1 Mark
Steps: 1 Mark
Result: 1 Mark
Let the first number be

9 x

Then, second consecutive number

= 9 (x + 1)

Third consecutive number

= 9 (x + 2)

,
And, fourth consecutive number

= 9 (x + 3)

According to question:

9 x + 9 (x + 1) + 9 (x + 2) + 9 (x + 3) = 378

\Rightarrow 9 x + 9 x + 9 + 9 x + 18 + 9 x + 27 = 378

\Rightarrow 36 x + 54 = 378

\Rightarrow 36 x = 378 - 54

\Rightarrow 36 x = 324

\Rightarrow x = \frac{324}{36} = 9

The numbers are 81, 90, 99 and 108.

Question 29. In thirteen years Gaurav will be twenty-four years old. Write the expression for Gaurav's age for 20 years from now. If after 20 years his father's age is 3 years less than 6 times Gaurav's present age. What is Gaurav's father's present age? [3 MARKS]

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:
Framing the equation: 1 Mark
Steps: 1 Mark
Result: 1 Mark
Let the present age of Gaurav be