NCERT Exercise 4.4 Solution
Simple Equations 7th Math
NCERT Exercise 4.4 Solution
Question (1) Set up equations and solve them to find the unknown numbers in the following cases:
Question (1)(a) Add 4 to eight times a number; you get 60.
Solution
Given, Add 4 to eight times a number; you get 60.
Let the number is m
Thus, eight times the number = 8 m
Thus, eight times a number + 4 = 60
⇒ 8 m + 4 = 60
Now, after subtracting 4 from both sides, we get
⇒ 8 m + 4 – 4 = 60 – 4
⇒ 8 m = 56
After dividing both sides by 8, we get
⇒ 8m/8 = 56/8
⇒ m = 7
Thus, number = 7 Answer
Alternate method to solve an equation
Given, Add 4 to eight times a number; you get 60.
Let the number is m
Thus, eight times the number = 8 m
Thus, eight times a number + 4 = 60
⇒ 8 m + 4 = 60
After transposing 4 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, +4 will become – 4 when transposed to RHS
⇒ 8 m = 60 – 4
⇒ 8 m = 56
After transposing 8 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 8 will become in division, i.e. goes to denominator after transposing to RHS
⇒ m = 56/8
⇒ m = 7
Thus, number = 7 Answer
Question (1)(b) One fifth of a number minus 4 gives 3.
Solution
Given, One fifth of a number minus 4 gives 3.
Let the number = m
Thus, according to question,
One fifth of a number – 4 = 3
⇒ 1/5 m – 4 = 3
After adding 4 to both sides we get
⇒ 1/5 m – 4 + 4 = 3 + 4
⇒ 1/5 m = 7
After multiplying both sides with 5, we get
⇒ 1/5 m × 5 = 7 × 5
⇒ m = 35
Thus, number = 35 Answer
Alternate method to solve an equation
Given, One fifth of a number minus 4 gives 3.
Let the number = m
Thus, according to question,
One fifth of a number – 4 = 3
⇒ 1/5 m – 4 = 3
After transposing –4 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, – 4 will become +4 when transposed to RHS
⇒ 1/5 m = 3 + 4
⇒ 1/5 m = 7
After transposing 5 to RHS
[When a digit or variable in denominator is transposed to other side, it is multiplied in other side]
Here, since 5 is in LHS in denominator, thus, it will become in multiplication in RHS
⇒ m = 7 × 5
⇒ m = 35
Thus, number = 35 Answer
Question (1)(c) If I take three forths of a number and count up 3 more, I get 21.
Solution
Given, If I take three forths of a number and count up 3 more, I get 21.
Let the number is m
Thus, according to question
3/4 m + 3 = 21
After subtracting 3 from both sides, we ge
⇒ 3/4 m + 3 –3 = 21 – 3
⇒ 3/4 m = 18
After multiplying both sides with 4, we get
⇒ 3/4 m ×4 = 18 × 4
⇒ 3 m = 72
After dividing both sides by 3, we get
⇒ 3m/3 = 72/3
⇒ m = 24
Thus, number = 24 Answer
Alternate method to solve an equation
Given, If I take three forths of a number and count up 3 more, I get 21.
Let the number is m
Thus, according to question
3/4 m + 3 = 21
After transposing 3 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, + 3 will become –3 when transposed to RHS
⇒ 3/4 m = 21 – 3
⇒ 3/4 m = 18
After transposing 4 to RHS
[When a digit or variable in denominator is transposed to other side, it is multiplied in other side]
Here, since 4 is in LHS in denominator, thus, it will become in multiplication in RHS
⇒ 3 m = 18 × 4
⇒ 3 m = 72
After transposing 3 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 3 will become in division, i.e. goes to denominator after transposing to RHS
⇒ m = 72/3
⇒ m = 24
Thus, number = 24 Answer
Question (1)(d) When I subtract 11 from twice a number, the result was 15.
Solution
Given, When I subtract 11 from twice a number, the result was 15.
Let the number is p
Thus, according to question,
Twice the number – 11 = 15
⇒ 2p – 11 = 15
After adding 11 to both sides, we get
⇒ 2 p – 11 + 11 = 15 + 11
⇒ 2p = 26
After dividing both sides by 2, we get
⇒ 2p/2 = 26/2
⇒ p = 13
Thus, number = 13 Answer
Alternate method to solve an equation
Given, When I subtract 11 from twice a number, the result was 15.
Let the number is p
Thus, according to question,
Twice the number – 11 = 15
⇒ 2p – 11 = 15
After transposing – 11 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, – 11 will become +11 when transposed to RHS
⇒ 2p = 15 + 11
⇒ 2p = 26
After transposing 2 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 2 will become in division, i.e. goes to denominator after transposing to RHS
⇒ p = 26/2
⇒ p = 13
Thus, number = 13 Answer
Question (1)(e) Munna subtracts thrice the number of notebooks he has from 50, he finds the result to be 8.
Solution
Given, Munna subtracts thrice the number of notebooks he has from 50, he finds the result to be 8.
Let the number of notebooks = n
Thus, according to question
50 – 3× number of notebooks = 8
⇒ 50 – 3n = 8
After subtracting 50 from both sides, we get
⇒ 50 – 3 n – 50 = 8 – 50
⇒ – 3n = – 42
⇒ 3 n = 42
After dividing both sides by 3, we get
⇒ 3n/3 = 42/3
⇒ n = 14
Thus, number of notebooks = 14 Answer
Alternate method to solve an equation
Given, Munna subtracts thrice the number of notebooks he has from 50, he finds the result to be 8.
Let the number of notebooks = n
Thus, according to question
50 – 3× number of notebooks = 8
⇒ 50 – 3n = 8
After transposing 50 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, +50 will become –50 when transposed to RHS
⇒ – 3n = 8 – 50
⇒ –3n = –42
⇒ 3n = 42
After transposing 3 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 3 will become in division, i.e. goes to denominator after transposing to RHS
⇒ n = 42/3
⇒ n = 14
Thus, number of notebooks = 14 Answer
Question (1)(f) Ibenhal thinks of a number. If she adds 19 to it and divides the sum by 5, she will get 8.
Solution
Given, Ibenhal thinks of a number. If she adds 19 to it and divides the sum by 5, she will get 8.
Let the number = n
Thus, according to question,
number + 19/5 = 8
⇒ n + 19/5 = 8
After multiplying both sides by 5, we get
⇒ n + 19/5 × 5 = 8 × 5
⇒ n + 19 = 40
After subtracting 19 from both sides, we get
⇒ n + 19 – 19 = 40 – 19
⇒ n = 21
Thus, number = 21 Answer
Alternate method to solve an equation
Given, Ibenhal thinks of a number. If she adds 19 to it and divides the sum by 5, she will get 8.
Let the number = n
Thus, according to question,
number + 19/5 = 8
⇒ n + 19/5 = 8
After transposing 5 to RHS
[When a digit or variable in denominator is transposed to other side, it is multiplied in other side]
Here, since 5 is in LHS in denominator, thus, it will become in multiplication in RHS
⇒ n + 19 = 8 × 5
⇒ n + 19 = 40
After transposing 19 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, +19 will become –19 when transposed to RHS
⇒ n = 40 – 19
⇒ n = 21
Thus, number = 21 Answer
Question (1)(g) Anwar thinks of a number. If he takes away 7 from 5/2 of the number, the result is 11/2
Solution
Given, Anwar thinks of a number. If he takes away 7 from 5/2 of the number, the result is 11/2
According to question,
5/2 × Number – 7 = 11/2
Let the number = n
Thus, 5/2 n – 7 = 11/2
After adding 7 to both sides, we get
⇒ 5/2 n – 7 + 7 = 11/2 + 7
⇒ 5/2 n = 11 + 14/2
⇒ 5/2 n = 25/2
After multiplying both sides by 2, we get
⇒ 5/2 n × 2 = 25/2 × 2
⇒ 5n = 25
After dividing both sides by 5, we get
⇒ 5n/5 = 25/5
⇒ n = 5
Thus, number = 5 Answer
Alternate method to solve an equation
Given, Anwar thinks of a number. If he takes away 7 from 5/2 of the number, the result is 11/2
According to question,
5/2 × Number – 7 = 11/2
Let the number = n
Thus, 5/2 n – 7 = 11/2
After transposing –7 to RHS
[When a digit or variable is transposed to other side, its sign changes]
Thus, –7 will become + 7 when transposed to RHS
⇒ 5/2 n = 11/2 + 7
5/2 n = 11 + 14/2
⇒ 5/2 n = 25/2
After transposing 2 to RHS
[When a digit or variable in denominator is transposed to other side, it is multiplied in other side]
Here, since 2 is in LHS in denominator, thus, it will become in multiplication in RHS
⇒ 5 n = 25/2 × 2
⇒ 5n = 25
After transposing 5 to RHS
[When a digit or variable in multiple goes to division after transposing to other side]
Here, 5 will become in division, i.e. goes to denominator after transposing to RHS
n = 25/5
⇒ n = 5
Thus, number = 5 Answer
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