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Question -

Set up equations and solve them to find the unknown numbers in the following cases:
(a) Add 4 to eight times a number; you get 60.
(b) One-fifth of a number minus 4 gives 3.
(c) If I take three-fourths of a number and add 3 to it, I get 21.
(d) When I subtracted 11 from twice a number, the result was 15.
(e) Munna subtracts thrice the number of notebooks he has from 50, he finds the result to be 8.
(f) Ibenhal thinks of a number. If she adds 19 to it and divides the sum by 5, she will get 8.
(g) Anwar thinks of a number. If he takes away 7 from 5/2 of the numbers, the result is 23.



Answer -

(a) Let the required number be x.
Step I: 8x + 4
Step II: 8x + 4 = 60 is the required equation
Solving the equation, we have
8x + 4 = 60
⇒ 8x = 60 – 4 (Transposing 4 to RHS)
⇒ 8x = 56
⇒ 8x/8=56/8 (Dividing both sides by 8)
⇒ x = 7
Thus, x – 7 is the required unknown number.
(b) Let the required number be x.
Step I: 1/5 x – 4
Step II: 1/5x – 4 = 3 is the required equation. 5
Solving the equation, we get
(c) Let the required number be x.
Step I: 3/4x + 3
Step II: 3/4x + 3 = 21 is the required equation.
Solving the equation, we have
⇒ x = 24 is the required unknown number.
(d) Let the required unknown number be x.
Step I: 2x – 11
Step II: 2x -11 = 15 is the required equations.
Solving the equation, we have
2x – 11= 15
⇒ 2x = 15 + 13 (Transposing 11 to RHS)
⇒ 2x = 28
⇒ 2x/2=28/2 (Dividing both sides by 2)
⇒ x = 14 is the required unknown number,
(e) Let the required number be x.
Step I: 50 – 3x
Step II: 50 – 3x = 8 is the required equations.
Solving the equation, we have
50 – 3x = 8
⇒ -3x = 8 – 50 (Transposing 50 to RHS)
⇒ -3x = -42
⇒ −3x/(−3)=−42/(−3) (Dividing both sides by -3)
⇒ x = 14 is the required unknown number.
(f) Let the required number be x.
Step I: x + 19
Step II:  
Step III:  = 8 is the required equation.
Solving the equation, we have
 = 8
 × 5 = 8 × 5(Multiplying both sides by 5)
⇒ x + 19 = 40
⇒ x = 40 – 19 (Transposing 19 to RHS)
∴ x = 21 is the required unknown number.
(g) Let the required number be x.
Step I: (5/2)x – 7
Step II: 5/5 – 7 = 23 is the required equation.
Solving the equation, we have

⇒ x = 12 is the required unknown number.

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