# Free Simple Equations 02 Practice Test - 7th grade

The sum of a number and its half is five less than twice the number. Which of the following equations represents given statement mathematically?

A.

x+x2 = (2x5)

B.

x+a2 = (52x)

C.

x+a2 = (52a)

D.

a+x2 = 2x5

#### SOLUTION

Solution : A

Let the number be 'x'.

Half of the number is x2.

Similarly, twice of the number =2x.

Sum of the number and its half =x+x2

5 less than twice the number =2x5

Given: Sum of the number and its half is five less than twice of the number.

The required equation is x+x2=2x5

If a=x then which number satisfies the equation: x+a2=(2x5)

A.

10

B.

5

C.

2

D.

7

#### SOLUTION

Solution : A

The equation in the above question is x+a2=(2x5)
We need to find the value of x.
Substituting the value 'x=a' and solving.

x+x2=(2x5)

3x2=(2x5)

2x3x2=5

x2=5

x=5×2

x=10

After buying a toy from the shop, I am left with 15 from my 100 rupees of pocket money. Then, the cost of toy (in rupees) is:

A.

15

B.

100

C.

85

D.

75

#### SOLUTION

Solution : C

Let the cost of the toy be x as it is the unknown.
x + 15 = 100

x = 100 - 15 = ₹85

So, the cost of the toy= ₹85

A shopkeeper has an unknown weight in his shop. To find out the weight, he first weighs 1 kg  of rice, and then weighs 1 kg of rice and the unknown weight together. The combined weight of the rice and the unknown weight is 1.5 kg. Find the unknown weight (in grams).

#### SOLUTION

Solution : Let the unknown weight be x kg
Given that,
weight of rice = 1 kg = 1000 g
weight of rice+unknown weight=1.5 kg                                                       =1500 g
x+1000 g=1500 g
x=(15001000)g=500 g
So, unknown weight = 500 g

Karan spends ₹ 5000 on food which is 58th of his income. Karan's income is ___ (in rupess).

#### SOLUTION

Solution :

Let Karan' s income be x
58  of x  = ₹ 5000
x= 5000×85
x =  ₹ (1000  x 8) = ₹ 8000

Pavani has a certain number of chocolates; she gave one-third of the chocolates to her brother Arjun, one-sixth to her friend Preeti. She was then left with 30 chocolates. What is the sum of the number of chocolates did she give to Arjun and Preeti?

___

#### SOLUTION

Solution : Let the number of chocolates Pavani has be x.
x3 are given to Arjun. So now she is left with xx3=2x3 chocolates

She gave x6 to Preeti. So, she is left with 2x3 - x6 = 4x6 - x6 = 3x6 = x2
So, x2=30
x=30×2=60

Initially, Pavani had 60 chocolates. She gave 13rd i.e. 603 =20 to Arjun.
16th i.e. 10 chocolates to Preeti.

Sum = 10 + 20 = 30

What is the value of x if 4x7=3x+5

A.

1

B.

12

C.

3

D.

5

#### SOLUTION

Solution : B

The given equation is,
4x7=3x+5
On transposing,
4x3x=7+5          x=12

In the equation x=10y24, sum of the coefficients of dependent and independent variables is ___.

#### SOLUTION

Solution :

The value of x depends on the value of y. So the dependent variable is x and the independent variable is y.

Sum of the coefficients of dependent and independent variable =(10+1)=11

The sum of three consecutive numbers is 36. Find the numbers.

A.

12,13,14

B.

10,11,12

C.

11,12,13

D.

13,12,11

#### SOLUTION

Solution : C

Let the first number be a.
So the three consecutive numbers will be a, a+1, a+2.

a +a +1 +a +2 = 36
3a +3 = 36
3a = 36 -3 = 33
a=333=11

So, the three consecutive numbers will be 11,12,13.

3x+15=10 is a simple equation. If 5 is added to the left-hand side of the equation, the equation remains the same as the given equation.

A.

True

B.

False

#### SOLUTION

Solution : B

If 5 is added to the left-hand side of the equation 3x+15=10, we get 3x+15+5=10.

The value on the left-hand side is increased but it remains same on the right-hand side. So, equality doesn't hold good now. 3x+15+510.
Equality sign remains unchanged only when same quantity is added on both sides, i.e., 3x+15+5=10+5.
Thus, the equation does not remain same as the given equation.