Representing Linear Equations for a Word Problem

Q. Half the perimeter of a rectangular garden, whose length is 8 m more than its width, is 40 m. Find the dimensions of the garden.

1. Length = 24m, Breadth = 16m
2. Length = 20m, Breadth = 18m
3. Length = 24m, Breadth = 20m
4. Length = 40m, Breadth = 36m

Q. If you represent the following statement in the form of a linear equation, which of the options are correct?
If we buy 2 tickets to station A and 5 tickets to station B, the total cost is Rs. 77.

1. 2x + 3y = 77
2. 3x + 2y = 77
3. 2x + 5y = 77
4. 5x + 2y = 77

Q.

The Coach of a cricket team buys 3 bats and 6 balls for Rs. 3900. Later, he buys another bat and 3 more balls of the same kind for Rs. 1300. Represent the situation algebraically.
[1 Mark]
[Introduction to pair of linear equations in two variables]

Q.

1. True

2. False

Q.

1. x+2y=0

2. x+y=0

3. 2x-y=0

4. x-2y=0

Q.

The sum of digits of a two-digit number is 10. The difference between the number and the number obtained by reversing the digits is 18. Find the appropriate equations.

1. x + y =11 ; y +2x =11

2. x +y =10; x + y = 10

3. x+y = 10 ; 2x +y =11

4. x + 2y = 10 ; 2x + y = 11

Q.

1. x+2y=0

2. x-2y=0

3. x+y=0

4. 2x-y=0

Q.

Adding 6 to numerator of a fraction , the numerator becomes twice the denominator. Which of the following equations represent this statement?

1. $x+6=2y$

2. $y+6=2x$

3. (a) and (b) above.
4. None of the above

Q.

A person travelling in an auto found that the fare of the journey consists of fixed charge together with the charge for the distance covered. The equation $x+10y=200$ represents , when the person travels 10 km. Find out the variable which represents the fixed charge in the equation.

__

Q.

10 times the numerator exceeds 5 times the denominator by 30. The equation satisfying the statement is

1. 10x – 5y = 30

2. 10y-5x = 30

3. Both (a) and (b)

4. None of these