3 Marks Question

Question 13 Marks

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 $77?$

Answer

Let the number of fruit trees be $x.$
According to the question,
$3 \times$ number of fruit trees $+ 2 =$ Number of non-fruit trees
We can write this as,
$3x + 2 = 77$
$3x = 77 – 2$
$3x = 75$
Now,
Dividing both sides by $3,$ we get:
$\frac{3 x}{3}=\frac{75}{3}$
Thus, $x = 25$
Hence, the number of fruit trees was $25.$

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Question 23 Marks

Laxmi’s father is $49$ years old. He is $4$ years older than $3$ times Laxmi’s age. What is Laxmi’s age$?$

Answer

Let Laxmi’s age $= x$ years
$4$ years more than $3$ times Laxmi’s age $= 4 + 3x$
Given Laxmi’s father age $= 49$
According to problem, $4 + 3x = 49$
$3x = 49 – 4 = 45$
$x = \frac{{45}}{3} = 15$
Hence the laxmi's age $= 15$ years.

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Question 33 Marks

Solve the equation by trial and error method: $3m – 14 = 4$

Answer

$L.H.S.$	Value of $m$	Value of $L.H.S.$	$R.H.S.$
$3m – 14$	$0$	$–14$	$4$
$3m – 14$	$1$	$–11$	$4$
$3m – 14$	$2$	$–8$	$4$
$3m – 14$	$3$	$–5$	$4$
$3m – 14$	$4$	$–2$	$4$
$3m – 14$	$5$	$1$	$4$
$3m – 14$	$6$	$4$	$4$

So, $m = 6$ is the solution of the given equation $3m – 14 = 4.$

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Question 43 Marks

Check whether the value given in the bracket is a solution to the given equation or not.
$7n + 5 = 19 (n = –2)$

Answer

$7n + 5 = 19 (n = –2)$
$L.H.S. = 7n + 5$
$= 7 (–2) + 5 . . . . [$ When $n = –2]$
$= –14 + 5$
$= –9$
$R.H.S. = 19$
$\because L.H.S. \neq R.H.S.$
$\therefore n = –2$ is not a solution to the given equation $7n + 5 = 19.$

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Question 53 Marks

Find a number, such that one-fourth of the number is $3$ more than $7.$

Answer

Let the unknown number to be $y.$
one-fourth of $y$ is $\frac{y}{4}$.
According to question,
This number $\left(\frac{y}{4}\right)$ is $3$ more than $7.$
Hence, the equation for $y$ is $\frac{y}{4}– 7 = 3$
Adding $7$ to the both sides of the equation, we get,
$\frac{y}{4}=3+7=10$
Multiply both sides of the equation by $4,$ we get,
$\frac{y}{4} \times 4=10 \times 4$
or $y = 40$

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Question 63 Marks

Raju’s father’s age is $5$ years more than three times Raju’s age. Find Raju’s age, if his father is $44$ years old.

Answer

Let Raju's age be $y$ years.
Three times Raju’s age is $3y$ years.
Raju’s father’s age is $5$ years more than $3y$
Therefore, Raju’s father's age $= (3y + 5)$ years
Also, given that Raju’s father is $44$ years old.
Therefore, $3y + 5 = 44.$
To solve it, we first transpose $5,$ to get
$3y = 44 – 5 = 39$
Dividing both sides by $3,$ we get $y = 13$
Therefore, Raju’s age is $13$ years.

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