Excercise 4.4 Simple-Equations - NCERT Solutions Class 7

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Chapter 4 Ex.4.4 Question 1

Set up equations and solve them to find the unknown numbers in the following cases:

(a) Add \(4\) to eight times a number; you get \(60\).

(b) One fifth of a number minus \(4\) gives \(3\).

(c) If I take three fourths of a number and add \(3\) to it, I get \(21\).

(d) When I subtracted \(11\) from twice a number, the result was \(15\).

(e) Munna subtracts thrice the number of notebooks he has from \(50\), he finds the result to be \(8\).

(f) Ibenhal thinks of a number. If she adds \(19\) to it and divides the sum by \(5\), she will get \(8\).

(g) Anwar thinks of a number. If he takes away \(7\) from \(\begin{align} \frac{5}{2}\end{align} \) of the number, the result is \(23\).

Solution

Video Solution

What is Known?

Statement of the Equation.

What is unknown?

Equation and the value of the variable which satisfy the equation.

Reasoning:

First read the statement of the question carefully suppose the number as any variable or alphabet then follow the steps given in the question.

Steps:

(a) Let the number be \(x\). According to the question,

\[\begin{align} 8x + 4 &= 60\\8x= 60 \,– 4 &= 56 \\ x = \frac{{56}}{8} &= 7\end{align}\]

(b) Let the number be \(y\). According to question,

\[\begin{align}\frac{y}{5} – 4 &=3\\ \frac{y}{5} &= 3 + 4\\ \frac{y}{5} &= 7\\ y&= 35\end{align}\]

(c) Let the number be \(x\). According to question,

\[\begin{align} \frac{3x}{4}+3&=21 \\  \frac{3x}{4}&=21-3 \\  \frac{3x}{4}&=18 \\  x&=\frac{18\times 4}{3} \\ x&=24 \\ \end{align}\]

(d) Let the number be \(x\). According to question,

\[\begin{align}2x- 11 &= 15\\2x &= 15 + 11\\2x &= 26\\ x &= \frac{{26}}{5} = 13\end{align} \]

(e) Let the number be \(x\). According to question,

\[\begin{align} 50 - 3x &= 8\\-3x = 8 \,– 50 &= -42\\x =\frac{{ - 42}}{{ - 3}} &= 14\end{align}\]

(f) Let the number be \(z\). According to question,

\[\begin{align} \frac{z + 19}{5} &= 8\\z + 19 &= 40\\z = 40 \,– 19 &= 21\end{align} \]

(g) Let the number be \(x\). According to question,

\[\begin{align}& \frac{5x}{2}~7=23~ \\ & ~\frac{5x}{2}=23+7~ \\ & \frac{5x}{2}~=30 \\ \end{align}\]

\[\begin{align}x = 30 \times \frac{2}{5} = 12\end{align}\]

Chapter 4 Ex.4.4 Question 2

Solve the following:

(a) The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus \(7\). The highest score is \(87\). What is the lowest score?

(b) In an isosceles triangle, the base angles are equal. The vertex angle is \(40^\circ\). What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is \(180^\circ\)).

(c) Smitha’s mother is \(34\) years old. Two years from now mother’s age will be \(4\) times Smitha’s present age. What is Smitha’s present age?

(d) Sachin scored twice as many runs as Rahul. Together, their runs fell two short of a double century. How many runs did each one score?

Solution

Video Solution

What is Known?

Statement of questions.

What is unknown?

Equation and the value of the variable.

Reasoning:

Make suitable equation using the given information and then solve the equation.

Steps:

(a) Highest score is \(87\). Let the lowest marks be \(x\)

According to question, highest marks obtained \(= 2x + 7\)

\[\begin{align}87 &= 2x + 7\\87 – 7 &= 2x\\80 &= 2x\\x &= 40\end{align}\]

(b) Let the base angle be \(b\). Since the triangle is isosceles, the other base angle will also be \(b\). Vertex angle is given \(40^\circ\).

Since, the sum of three angles of a triangle \(= 180^\circ\)

\[\begin{align}b + b + 40^\circ &= 180^\circ\\2b + 40^\circ &= 180^\circ\\2b = 180^\circ - 40^\circ &= 140^\circ\\b = \frac{140}{2} &= 70^\circ\end{align}\]

(c) Let the present age of Smitha be \(x\). Age of her mother \(= 34\) years

Two years from now Smitha age will be \(= x + 2\)

According to question,

\[\begin{align}4(x + 2) &= 34\\4x + 8 &= 34\\4x &= 34 - 8 = 16\\x &= 4\end{align}\]

(d) Let the score of Rahul be \(x\), and score of Sachin be \(2x\)

According to question,

\[\begin{align}x + 2x &= 198\\3x &= 198\\x &= \frac{{198}}{3}= 66\end{align}\]

So, Rahul’s score \(= 66\) runs

And. Sachin’s score \(= 2x = 132\) runs

Chapter 4 Ex.4.4 Question 3

Solve the following:

(a) Irfan says that he has \(7\) marbles more than five times the marbles Parmit has. Irfan has \(37\) marbles. How many marbles does Parmit have?

(b) Laxmi's father is \(49\) years old. He is \(4\) years older than three times Laxmi's age. What is Laxmi's age?

(c) People of Sundargram planted trees in the village garden. Some of the trees were fruit trees. The number of non-fruit trees were two more than three times the number of fruit trees. What was the number of fruit trees planted if the number of non-fruit trees planted was \(77\)?

Solution

Video Solution

What is known?

Statement of the question.

What is unknown?

Equation and the value of the variable.

Reasoning:

Make suitable equation using the given information and then solve the equation.

Steps:

(a) Number of marbles Parmit has \(37\). Let the number of marbles Parmit has be \(x\). According to question,

\[\begin{align}5x  + 7 &= 37\\5x &= 30\\x = \frac{{30}}{5} &= 6\end{align}\]

Therefore, Parmit has \(7\) marbles

(b) Let the age of Laxmi be \(x\). Age of Laxmi’s father be \( 49\) years

According to question,

\[\begin{align}3x + 4 &= 49\\3x = 49 \,– 4 &= 45\\x = \frac{{45}}{3} &= 15\end{align}\]

Therefore, Laxmi’s age is \(15\) years

(c) Let the number of fruit tress be \(x\). Then the number of non-fruit trees are \(3x +2\)

According to question,

\[\begin{align}3x + 2 &= 77\\3x = 77 - 2&= 75\\x = \frac{{75}}{3} &= 25\end{align}\]

The number of fruit trees planted are \(25\).

Chapter 4 Ex.4.4 Question 4

Solve the following riddle:

I am a number, 

Tell my identity!

Take me seven times over 

And add a fifty!

To reach a triple century 

You still need forty!

Solution

Video Solution

What is Known?

A riddle.

What is unknown?

The number in the riddle.

Reasoning:

Use the given information to make an equation with unknown number as a variable. Solve the equation to get value of the number.

Steps:

Let the number be \( x\).

According to question,

\[\begin{align}7x + 50 + 40 &= 300\\7x &= 300 - 90\\7x &= 210\\x = \frac{{210}}{7}&= 30\end{align}\]

Therefore, the number is \(30\)

  
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