19. The sum of two numbers is 60 and their difference is 30.
(a) If smaller number is x, the other number is ________ (use sum).
(b) The difference of numbers in term of x is ________.
(c) The equation formed is ________.
(d) The solution of the equation is ________.
(e) The numbers are ________ and ________.
(a) 60 − x
(b) 60 − 2x
(c) −2x = −30
(d) 15
(e) 45 and 15
20. Sum of two numbers is 81. One is twice the other.
(a) If smaller number is x, the other number is ________.
(b) The equation formed is ________.
(c) The solution of the equation is ________.
(d) The numbers are ________ and ________.
(a) 2x
(b) x + 2x = 81
(c) 27
(d) 54 and 27
21. In a test Abha gets twice the marks as that of Palak. Two times Abha's marks and three times Palak's marks make 280.
(a) If Palak gets x marks, Abha gets ________ marks.
(b) The equation formed is ________.
(c) The solution of the equation is ________.
(d) Marks obtained by Abha are ________.
(a) 2x
(b) 4x + 3x = 280
(c) 40
(d) 80
22. The length of a rectangle is two times its breadth. Its perimeter is 60 cm.
(a) If the breadth of rectangle is x cm, the length of the rectangle is ________.
(b) Perimeter in terms of x is ________.
(c) The equation formed is ________.
(d) The solution of the equation is ________.
(a) 2x
(b) 6x or 2(2x + x)
(c) 6x = 60
(d) 10
23. In a bag there are 5 and 2 rupee coins. If they are equal in number and their worth is ₹70, then
(a) The worth of x coins of ₹5 each ________.
(b) The worth of x coins of ₹2 each ________.
(c) The equation formed is ________.
(d) There are ________ 5 rupee coins and ________ 2 rupee coins.
(a) ₹5x
(b) ₹2x
(c) 5x + 2x = 70
(d) 10, 10
24. In a Mathematics quiz, 30 prizes consisting of 1st and 2nd prizes only are to be given. 1st and 2nd prizes are worth ₹2000 and ₹1000, respectively. If the total prize money is ₹52,000 then show that:
(a) If 1st prizes are x in number the number of 2nd prizes are ________.
(b) The total value of prizes in terms of x are ________.
(c) The equation formed is ________.
(d) The solution of the equation is ________.
(e) The number of 1st prizes are ________ and the number of 2nd prizes are ________.
(a) 30 − x
(b) 2000x + 1000(30 − x)
(c) 1000x + 30000 = 52000
(d) 22
(e) 22, 8
If z + 3 = 5, then z = ________.
If z + 3 = 5, then z = 2.
________ is the solution of the equation 3x − 2 = 7.
x = 3 is the solution.
________ is the solution of 3x + 10 = 7.
x = −1 is the solution.
If 2x + 3 = 5, then value of 3x + 2 is ________.
5
In integers, 4x − 1 = 8 has ________ solution.
No solution.
In natural numbers, 4x + 5 = −7 has ________ solution.
No solution.
In natural numbers, x − 5 = −5 has ________ solution.
No solution.
In whole numbers, x + 8 = 12 − 4 has ________ solution.
One solution.
If 5 is added to three times a number, it becomes the same as 7 is subtracted from four times the same number. This fact can be represented as ________.
3x + 5 = 4x − 7
x + 7 = 10 has the solution ________.
x = 3
x − 0 = ________; when 3x = 12.
4
x − 1 = ________; when 2x = 2.
0
x − ________ = 15; when x/2 = 6.
−3
The solution of the equation x + 15 = 19 is ________.
4
Finding the value of a variable in a linear equation that ________ the equation is called a ________ of the equation.
Finding the value of a variable in a linear equation that satisfies the equation is called a root of the equation.
Any term of an equation may be transposed from one side of the equation to the other side of the equation by changing the ________ of the term.
sign
If 9/5 x = 18/5, then x = ________.
2
If 3 − x = −4, then x = ________.
7
If x − 1/2 = −1/2, then x = ________.
0
If 1/6 − x = 1/6, then x = ________.
0
If 10 less than a number is 65, then the number is ________.
75
If a number is increased by 20, it becomes 45. Then the number is ________.
25
If 84 exceeds another number by 12, then the other number is ________.
72
If x − 7/8 = 7/8, then x = ________.
7/4