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
(f) Notebooks he has from 50, he finds the result to be 8.
(g) Ibenhal thinks of a number. If she adds 19 to it and divides the sum by 5, she will get 8.
(h) Anwar thinks of a number. If he takes away 7 from of the number, the result is 23.
The parts of this given questions are solved below:
(a) We have to frame the equation on the basis of given statement
And then solve the so framed equation
Thus,
Let the number be a
We know that,
Eight times of a is 8a
Therefore,
As per the statement,
We can write the equation as,
8a + 4 = 60
8a = 60 – 4
8a = 56
Now,
Dividing 8 on both the sides, we get
Therefore,
a = 7
(b) We have to frame the equation on the basis of given statement
And then solve the so framed equation
Thus,
Let the number be a
We know that,
One fifth of a is
Therefore,
As per the statement,
We can write the equation as,
= 3 + 4
= 7
Now,
Multiplying 5 to both the sides, we get
Therefore,
a = 35
(c) We have to frame the equation on the basis of given statement
And then solve the so framed equation
Thus,
Let the number be a
We know that,
Three fourth of a is
Therefore,
As per the statement,
We can write the equation as,
= 21 – 3
= 18
Now,
Multiplying to both the sides, we get
Therefore,
a = 24
(d) We have to frame the equation on the basis of given statement
And then solve the so framed equation
Thus,
Let the number be a
We know that,
Twice of a is 2a
Therefore,
As per the statement,
We can write the equation as,
2a – 11 = 15
2a = 15 + 11
2a = 26
Now,
Dividing 2 on both the sides, we get
Therefore,
a = 13
(e) We have to frame the equation on the basis of given statement
And then solve the so framed equation
Thus,
Let the number be a
We know that,
Thrice of a is 3a
Therefore,
As per the statement,
We can write the equation as,
50 – 3a = 8
-3a = 8 – 50
-3a = -42
Now,
Dividing -3 on both the sides, we get
Therefore,
a = 14
(f) We have to frame the equation on the basis of given statement
And then solve the so framed equation
Thus,
Let the number be a
Therefore,
As per the statement,
We can write the equation as,
Now,
Multiplying 5 to both the sides, we get
Therefore,
a + 19 = 40
a = 40 – 19
a = 21
(g) We have to frame the equation on the basis of given statement
And then solve the so framed equation
Thus,
Let the number be a
We know that,
of a is
Therefore,
As per the statement,
We can write the equation as,
= 23 + 7
= 30
Now,
Multiplying to both the sides, we get
Therefore,
a = 12