Free Simple Equations 03 Practice Test - 7th grade

Question 1

$x + 3 = 8$ is called an algebraic ______.

variable

expression

equation

statement

SOLUTION

Solution : C

An algebraic expression having an equality sign is called an equation. An equation is a constraint placed on a variable which is in an expression.

Question 2

The value of $y$ that satisfies the equation $3 (y + 2) = 12$ is

$4$

$2$

$3$

$7$

SOLUTION

Solution : B

$3 (y + 2) = 12$
Dividing both the sides of the equation by 3,
$\frac{3 (y + 2)}{3} = \frac{12}{3} y + 2 = 4$
Subtracting 2 from both the sides of the equation,
$y + 2 - 2 = 4 - 2$
$∴ y = 2$

Question 3

Frame an equation for the statement: "A number is four times another number and their difference is 12".

x + 4 x = 12

4 x - x = 12

4 x = 12

5 x = 15

SOLUTION

Solution : B

$Let the number be x .$
$The other number is four times x, that is 4 x .$

$Difference between them is 12: \Rightarrow (4 x - x) = 12$

$Hence, the required equation is 4 x - x = 12.$

Question 4

Tony scored twice as many runs as Kohli. Together they scored $6$ runs short of triple century. How many runs did each score?

$196, 98$

$96, 192$

$19, 38$

$250, 125$

SOLUTION

Solution : A

Runs scored by Kohli be $x$ . Then, runs scored by Tony will be $2 x$ .

$2 x + x = 300 - 6 = 294$
$3 x = 294$
$x = \frac{294}{3} = 98$
$So, Kohli scores 98 and Tony scores 196 runs.$

Question 5

For the equation: $3 z + \frac{7}{2}$ = $\frac{5}{2}$ , ' $z$ ' is equal to ____.

$\frac{1}{3}$

$\frac{- 1}{3}$

$\frac{- 2}{3}$

$\frac{2}{3}$

SOLUTION

Solution : B

$3 z + \frac{7}{2} = \frac{5}{2}$

$\frac{6 z + 7}{2} = \frac{5}{2}$ (by taking the LCM)

$\frac{6 z + 7}{2} \times 2 = \frac{5}{2} \times 2$

$6 z + 7 = 5$

$6 z + 7 - 7 = 5 - 7$

$6 z = - 2$

$\frac{6 z}{6} = \frac{- 2}{6}$

$∴ z = \frac{- 1}{3}$

Question 6

If a certain number when decreased by $21$ becomes $81$ , what is the number?

___

SOLUTION

Solution :
$Let the number be x.$
$x - 21 = 81$
$x = 102$

Question 7

7 years hence, Sarosh's father age will be thrice that of Sarosh's age. Presently father's age is 6 times of Sarosh's age. Sum of their present ages is equal to:

___

SOLUTION

Solution : Let Sarosh's present age be $x$ .
After 7 years Sarosh's age will be $x + 7$
and, his father's age will be $3 (x + 7)$ .
This is equal to 6 times Sarosh's present age, i.e. $= 6 x$
So,
$6 x = 3 (x + 7) = 3 x + 21$
$6 x - 3 x = 21$
$3 x = 21$
$x = 7$
Sarosh's present age is 7 years.

Father's age after 7 years is,
$6 \times 7 = 42 y e a r s$
His present age is,
$42 - 7 = 35 y e a r s$

$Sum of their present ages = 35 + 7 = 42$

Question 8

Is $4 x + 5 - y = 0$ a linear equation in one variable?

True

False

SOLUTION

Solution : B

$4 x + 5 - y = 0$ has two variables x and y.

Therefore, $4 x + 5 - y$ is an equation in two variables.

Question 9

$x = 3$ is the solution of the equation $x + 3 = 0$ .

True

False

SOLUTION

Solution : B

The value of unknown variable which satisfies the equation is called solution of the equation.

So, substituting $x = 3$ , we get $3 + 3$ i.e. $6$ which is not equal to zero. So, $3$ is not the solution of the equation.

Question 10

Raju reads $\frac{2}{3}$ rd of a book. He finds that still there are 100 pages to be read. The total number of pages in the book are?

SOLUTION

Solution :
If Raju reads $\frac{2}{3}$ rd of a book. He will still have
$\frac{1}{3}$ rd of the book to complete.
Let the total number of pages of the book be y
Then $\frac{1}{3} y = 100$
Hence y = 3 $\times$ 100
= 300

Free Simple Equations 03 Practice Test - 7th grade

Question 1

SOLUTION

Question 2

SOLUTION

Question 3

SOLUTION

Question 4

SOLUTION

Question 5

SOLUTION

Question 6

SOLUTION

Question 7

SOLUTION

Question 8

SOLUTION

Question 9

SOLUTION

Question 10

SOLUTION

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