Conversion of Statements to Linear Equations

Q.

2/3x-3/2x=1/12

Q.

The sum of two numbers is 70. Their difference is 16 . Find the numbers.

Q.

Minal and Raj have to collect different kinds of leaves for a science project. They go to a park where Minal collects 12 leaves and Raj collects x leaves. After some time Minal loses 3 leaves and Raj collects 2x leaves. Write an algebraic expression to find the total number of leaves collected by both of them.

1. 9 + 3x
2. 9x + 3
3. 12x - 3
4. 12 - 5x

Q.

A two digit number $xy$ can be represented as

1. $x+y$
2. $10x+y$
3. $x^y$

4. $2x+y$

Q.

Amina thinks a number and subtracts 5/2 from it.she multiply the result by 8. the result now obtained is three times the same number she thought of. what is the number?

Q.

A two digit number is such that the sum of itself and the number obtained when its digits are reversed is 55. Using the given data, write the simplest equation possible in two variables.

1. $x+\frac{1}{x}=55$

2. $x+5=y$

3. $x+y=5$

4. $2x+2y=55$

Q.

Simplify:

(2x - 3)(5x + 2) + (3x - 7)(4x - 1)

Q. A train runs constantly at a speed of 120 km/hr.
Draw a time – distance graph for this situation. Find the
(i) time taken to cover 360 km.
(ii) distance covered in $6\frac{1}{2}$ hours.

1. 2 hrs and 780 km
2. 2 hrs and 720 km
3. 3 hrs and 780 km
4. 3 hrs and 720 km

Q.

One more than twice the number. Give corresponding Expression.

Q.

In each of the problems below the result of doing some operation on a number is given. Find the number?

1). $3$ added to double is $101.$

2). $2$ added to triple is $101.$

3). $3$ subtracted from double is $101.$

4). $2$ subtracted from triple is $101.$

Q. Question 3(iii)
For an experiment in Botany, two different plants, plant A and plant B were grown under similar laboratory conditions. Their heights were measured at the end of each week for 3 weeks. The results are shown by the following graph.

How much did Plant A grow during the $3^{rd}$ week?

Q.

Question 13

In the following question out of the four options only one is correct, write the correct answer.

The digit in the ten's place of a two-digit number is 3 more than the digit in the unit's place. Let the digit at unit's place be b. Then, the number is:

(a)11b + 30

(b) 10b + 30

(c) 11b + 3

(d) 10b + 3

Q.

7X/2+X/4+X/8=11

Q. Question 3(iv)
For an experiment in Botany, two different plants, plant A and plant B were grown under similar laboratory conditions. Their heights were measured at the end of each week for 3 weeks. The results are shown by the following graph.

How much did Plant B grow from the end of the $2^{nd}$ week to the end of the $3^{rd}$ week?

Q.

(x÷3)+(2x÷3)+(x÷4)=10

Q.

Amina thinks of a new number and subtracts 5/2 from IT .she multiply the result by 8 the result now obtained is three times the same number thought of what is the number

Q. By what number should (−3)⁻¹ be multiplied so that the product becomes 6⁻¹?

Q.

Draw a graph for the radius and circumference of the circle using a suitable scale. (Hint: Take radius = 7, 14, 21 units, and so on) From the graph, (a) Find the circumference of the circle when the radius is 42 units. (b) At what radius will the circumference of the circle be 220 units?

Q. Use direct method (x+8)(x+3)

Q.

Find a no. Such that when 5 is subtracted from 5 times a no. The result is 4 more twice the no.?

Q.

Convert the following expressions into statements$.$

$\frac{7}{10}x-5$

Q. Three hourly rental car companies I, II, and III charge customers based on the time duration for which they book a car along with the fixed basic pay for booking for a day.
Company I:


Company II:
$\begin{array}{cc}\text{Travel time}& \text{Booking price}\left(\$\right),y\\ \text{(in hr), x}& \\ 0& 10\\ 3& 31\\ 5& 45\\ 7& 59\end{array}$

Company III: Charges fixed pay of $\$12$ and its hourly price is an integer between hourly prices of company I and company II.
If you want to book for 6 hours, which rental car company would you choose?
Assume you will choose the company which is charging you the lowest price of booking.

1. Company II
2. Either Company I or III
3. Company III
4. Company I

Q. Choose the correct option which represents the following statement as an expression.

Two times of a number x is added to 5.

1. 2x+5
2. 2x-5
3. 4x+15
4. 2x-8

Q.

A positive number is 5 times another number. If 21 is added to both the numbers then one of the new numbers becomes twice the other new number. What are the numbers?

Q.

3(t-3)=5(3t+1)

Q.

Write the statement for each of the following

$\frac{x}{3}=4$

Q.

(2x+3/3)-(5x-3/6)=×-3/2

Q. Choose the correct option which represents the following statement as an expression.

Three times of a number x, is added to 4.

1. 2x+4
2. 3x+4
3. 3x-4
4. 2x-4

Q.

A and B have certain amount of money. The sum of twice the amount A has and thrice the amount B has is equal to ₹ 1500.
How do you represent this as an equation?
[Consider, A has "$₹a$" and B has "$₹b$" amount of money.]

1. $2a=3b+1500$

2. $2a+3b=1500$

3. $3a-2b=1500$

4. $2a+2a+3b+3b=1500$

Q.

Write the expression in words for $16=5x+1$