Representing Linear Equations for a Word Problem

Q. the sum of the numerator the denominator ofa fraction is 4 more than twice the numerator if 3 is added to each of the numerator and denominator their ratio becomes 2:3. find the fraction

Q. The parking charges of a car in a parking lot are Rs.30 for the first two hours and Rs.10 for subsequent hours. Taking total parking time to be X hours and total charges as y, write a linear equation in two variables to express the above statement. Draw a graph for the linear equation and tell the charges for five hours.

Q.

In an envelope there are some $5$ rupee notes and some $10$ rupee notes. Total amount of these notes together is $350$ rupees. Number of $5$ rupee notes are greater by $10$ than number of $10$ rupee notes. Then find the number of $5$ rupee and $10$ rupee notes.

Q. The total cost of 8 books and 5 pens is $₹420$ and the total cost of 5 books and 8 pens is ₹321. Find the cost of 1 book and 2 pens.

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 = 10 ; 2x +y =11

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

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

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

Q.

Write “$3$ times a number $y$ is $42$” as an equation. Then solve the equation.

Q.

The difference of areas of two squares is A. The difference of their perimeters is P. The sum of their perimeters is

1. $\frac{2A}{P}$

2. $\frac{4A}{P}$

3. $\frac{8A}{P}$

4. $\frac{16A}{P}$

Q. A and B each have a certain number of mangoes. A says to B "If you give me 30 of your mangoes, I will have twice as many as left with you." B replies, "If you give me 10, I will have thrice as many as left with you." How many mangoes does each have ?

Q. 10.The cost of a notebook is Rs 5 less than twice the cost of a pen .
Write this statement as a linear equation in two variables.

Q.

The difference of areas of two squares is A. The difference of their perimeters is P. The sum of their perimeters is

1. $\frac{2A}{P}$

2. $\frac{4A}{P}$

3. $\frac{8A}{P}$

4. $\frac{16A}{P}$

Q. The boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of stream and that of the boating till water.

1. Speed of boat = 8 km/h & Speed of stream $=3$ km/hr
2. Speed of boat = 8 km/h & Speed of stream $=4$ km/hr
3. Speed of boat = 7 km/h & Speed of stream $=2$ km/hr
4. Data insufficient

Q. Find the values of $x$ and $y$ in the following rectangle.

[2 Marks]

Q. Adding 6 to numerator of a fraction , the numerator becomes twice the denominator. Write the equation(s) that represent the given statement.

Q. 5. Fixed price in a taxi is ruppes x and charged per km is ruppes y.if Fair for 10km is ruppes 70, then write the given data in the form of a linear equation in two variables. Also represent it graphically.what will the fixed charges , if charges per km are rupees 5 ?

Q.

The sum of the numerator and denominator of a fraction is 4 more than twice the numerator.If the numerator and denominator are increased by 3, they are in the ratio 2:3.Determine the fraction.

Q.

1. x+2y=0

2. x+y=0

3. 2x-y=0

4. x-2y=0

Q. On expressing the equation $5x+2y=28$ in the general form of a linear equation in two variables $ax+by+c=0,$ the value of $c$ equals .

Q. CHAPTER NAME : Simultaneous Linear Equations
​5. The sum of the digits of a two-digit number is 5. If 9 is added to the number, the digits are interchanged. Find the number.

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.

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

1. None of the above

2. $y+6=2x$

3. (a) and (b) above.

4. $x+6=2y$

Q.

1. The present age of Jacob and his son are x years and y years respectively. Five years hence, the age of Jacob will be three times that of his son. Write a linear equation for this information

Q.

There are a few families residing in a localty.For a festival some families donated Rs 100 each the other families donated Rs 50 each.The total money collected was Rs 44, 450.Express this in the form of an equation in two variables.Using this equation , find the no. of families who donated Rs 100 each if the no. of families donating Rs 50 is 111

Q. Form the pair of linear equations from the following information: Sachin tells his daughter. "Seven years ago, I was seven times as old as you were then. Also three years from now, I shall be three times as old as you will be."

Q.

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

1. (a) and (b) above.

2. $y+6=2x$

3. $x+6=2y$

4. None of the above

Q. A number consists of two digits. The digit in tens place exceeds the digit in units place by 4. The sum of the digits is 1/7 of the number. Find the number.

Q. $-$x = 5, $-$5 < y

Q. A fraction is such that if the numerator is multiplied by 3 and the denominator is reduced by 3, we get $\frac{8}{11}$, but if the numerator is increased by 8 and the denominator is doubled, we get $\frac{2}{5}$. Find the fraction.

Q.

The cost of toy telephone is same as cost of 4 balls . Express statement as a linear equation in two variable.also find the cost of getting 2 toy telephone packed if cost of 1 ball is Rs 5 and there is fined cost of Rs 2 for packing a toy telephone

Q.

Any two digit number can be represented as

___x + y

Q.

A number consist of 2 digit.The digit in tens place exceeds the digit in ones place by 2.The difference of digits is 1/32 of the number.Find the number